3x^2+4x-6=0

Simple and best practice solution for 3x^2+4x-6=0 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 3x^2+4x-6=0 equation:


Simplifying
3x2 + 4x + -6 = 0

Reorder the terms:
-6 + 4x + 3x2 = 0

Solving
-6 + 4x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.333333333x + x2 = 0 + 2
1.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.333333333x + x2 = 2

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 2 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 2 + 0.4444444442

Combine like terms: 2 + 0.4444444442 = 2.4444444442
0.4444444442 + 1.333333333x + x2 = 2.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 2.4444444442

Calculate the square root of the right side: 1.56347192

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.56347192 and -1.56347192.

Subproblem 1

x + 0.6666666665 = 1.56347192 Simplifying x + 0.6666666665 = 1.56347192 Reorder the terms: 0.6666666665 + x = 1.56347192 Solving 0.6666666665 + x = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.56347192 + -0.6666666665 x = 1.56347192 + -0.6666666665 Combine like terms: 1.56347192 + -0.6666666665 = 0.8968052535 x = 0.8968052535 Simplifying x = 0.8968052535

Subproblem 2

x + 0.6666666665 = -1.56347192 Simplifying x + 0.6666666665 = -1.56347192 Reorder the terms: 0.6666666665 + x = -1.56347192 Solving 0.6666666665 + x = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.56347192 + -0.6666666665 x = -1.56347192 + -0.6666666665 Combine like terms: -1.56347192 + -0.6666666665 = -2.2301385865 x = -2.2301385865 Simplifying x = -2.2301385865

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8968052535, -2.2301385865}

See similar equations:

| 27=a+5a | | 2800=(11*140)+(9*60)+180m | | 5(y+2)-y= | | 3x+y=2 | | 5x+135=25 | | 7(8n+12)=7(1+6n) | | 12n-147=4n-11 | | x^2+10x=10 | | x^3-7x^2+13x-15=0 | | 2n-147=4n-11 | | 2200=450+(2*450)+x | | (T+8)(-2)=12 | | 2x^4-5x^3-3x^2=0 | | 3838x^8383=38833929283821883 | | -4(t-1)+8t=6t-9 | | 47-6x=3x+19 | | 11-9x=93-23x | | -3u-w=u+5w | | -106-9x=9x+20 | | 30-0.5x=2x-15 | | 10+3y-2=4y-y+8 | | 32x^3=546 | | 105-5x=3x+17 | | 23x-3=22x+3 | | -18-5x=12-8x | | x^2+6=-7x | | x*2+7=11 | | 21-6x=-21 | | 9+8m=81 | | -8x-17=7 | | -2x^2+3x+5=0 | | 3x^3=528 |

Equations solver categories