0=3x^2+5x-3

Simple and best practice solution for 0=3x^2+5x-3 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 0=3x^2+5x-3 equation:


Simplifying
0 = 3x2 + 5x + -3

Reorder the terms:
0 = -3 + 5x + 3x2

Solving
0 = -3 + 5x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -5x + -3x2 = -3 + 5x + 3x2 + 3 + -5x + -3x2

Reorder the terms:
3 + -5x + -3x2 = -3 + 3 + 5x + -5x + 3x2 + -3x2

Combine like terms: -3 + 3 = 0
3 + -5x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2
3 + -5x + -3x2 = 5x + -5x + 3x2 + -3x2

Combine like terms: 5x + -5x = 0
3 + -5x + -3x2 = 0 + 3x2 + -3x2
3 + -5x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
3 + -5x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.666666667x + x2 = 0 + 1
1.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.666666667x + x2 = 1

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 1 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 1 + 0.6944444447

Combine like terms: 1 + 0.6944444447 = 1.6944444447
0.6944444447 + 1.666666667x + x2 = 1.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 1.6944444447

Calculate the square root of the right side: 1.301708279

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.301708279 and -1.301708279.

Subproblem 1

x + 0.8333333335 = 1.301708279 Simplifying x + 0.8333333335 = 1.301708279 Reorder the terms: 0.8333333335 + x = 1.301708279 Solving 0.8333333335 + x = 1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.301708279 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.301708279 + -0.8333333335 x = 1.301708279 + -0.8333333335 Combine like terms: 1.301708279 + -0.8333333335 = 0.4683749455 x = 0.4683749455 Simplifying x = 0.4683749455

Subproblem 2

x + 0.8333333335 = -1.301708279 Simplifying x + 0.8333333335 = -1.301708279 Reorder the terms: 0.8333333335 + x = -1.301708279 Solving 0.8333333335 + x = -1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.301708279 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.301708279 + -0.8333333335 x = -1.301708279 + -0.8333333335 Combine like terms: -1.301708279 + -0.8333333335 = -2.1350416125 x = -2.1350416125 Simplifying x = -2.1350416125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4683749455, -2.1350416125}

See similar equations:

| 3cos^2x+8sinx=7 | | 3x+12=52-3x | | 4[4x-2(y-2)]= | | 5(x+2)=3(x-2)+2(x+8) | | 5/6x+5/9-3/7x=0 | | 3x-10=-3x+20 | | w^2+3w=10 | | 2cos^2x-cosx=0 | | 7e^3x+6=11 | | 4x+15=-2x-15 | | 2x-3y=07 | | X+7=25+4x | | x^2+22x+44=0 | | y+4=-2/5(x-15) | | -2/5(x-15) | | X-y=678.24 | | 7x+18=-2x | | -3+4x=77 | | 7+4x+7x=-59 | | 1/4d+3=13 | | 7+4x+7x=59 | | 8(x+2)=6(x-2)+2(x+14) | | 1/2(z-(4/5))=-(1/6)(z+4) | | 6+(3-x/2)=1 | | 3=5x-2x+3 | | 3=5x-2x+3 | | x-0+0x-1=0 | | (8y^3-y^2+3)(5y^2+y+1)= | | 1/2(z-(4/4))=-(1/6)(z+4) | | 13=5x-5 | | 5x-16=-11 | | -2/3t-2-3 |

Equations solver categories