6x-3=2x^2

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


Simplifying
6x + -3 = 2x2

Reorder the terms:
-3 + 6x = 2x2

Solving
-3 + 6x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
-3 + 6x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -3x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -3x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3x + x2 = 0 + -1.5
-3x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-3x + x2 = -1.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -1.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -1.5 + 2.25

Combine like terms: -1.5 + 2.25 = 0.75
2.25 + -3x + x2 = 0.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(x + -1.5) equal to 0.866025404 and -0.866025404.

Subproblem 1

x + -1.5 = 0.866025404 Simplifying x + -1.5 = 0.866025404 Reorder the terms: -1.5 + x = 0.866025404 Solving -1.5 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.866025404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.866025404 + 1.5 x = 0.866025404 + 1.5 Combine like terms: 0.866025404 + 1.5 = 2.366025404 x = 2.366025404 Simplifying x = 2.366025404

Subproblem 2

x + -1.5 = -0.866025404 Simplifying x + -1.5 = -0.866025404 Reorder the terms: -1.5 + x = -0.866025404 Solving -1.5 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.866025404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.866025404 + 1.5 x = -0.866025404 + 1.5 Combine like terms: -0.866025404 + 1.5 = 0.633974596 x = 0.633974596 Simplifying x = 0.633974596

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.366025404, 0.633974596}

See similar equations:

| 5-2n=3-n | | 5t-(2T+14)=3T-14 | | 3(-6)+6(-6)=3-9 | | 14+2(11-h)=-5 | | -2(4b+2)+(9b-4)=0 | | 4t^2-25t+6=0 | | 5(-x-5)=-30 | | -1550-7x=1718 | | 3(x+4)=5x+16 | | 6h-117=-21 | | 8(x+2)+1=4x+4(4+x) | | 3(5x+6)+5(3x+3)+3=30x+37 | | 8x-1=9x-5 | | 39(x+4)=5x+16 | | 5-2y=3x | | 118.8-7.7x=3.3+39.6 | | 8=-5y-2 | | 2/3-7= | | -5n+x=78 | | 8(2n-3)=(2n+8)+3 | | 5x+5x+4+8=7x+4+2x | | -3(t+4)=3 | | 3(2-z)*0.2=z | | (3x)+4=-11 | | 11(2+8x)-10(10-11x)=912 | | -2(x-18)=(-x/2+3)(-3) | | 12=4n-10 | | x^3=216 | | -5=-x+3 | | 6x+2+3x+17=10 | | 3n+6n=3-9 | | .6a-.75b=c |

Equations solver categories