3x^2+4x-12=0

Simple and best practice solution for 3x^2+4x-12=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-12=0 equation: 


Simplifying
3x2 + 4x + -12 = 0

Reorder the terms:
-12 + 4x + 3x2 = 0

Solving
-12 + 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'.
-4 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.333333333x + x2 = 0 + 4
1.333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.333333333x + x2 = 4

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 = 4 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 4 + 0.4444444442

Combine like terms: 4 + 0.4444444442 = 4.4444444442
0.4444444442 + 1.333333333x + x2 = 4.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 4.4444444442

Calculate the square root of the right side: 2.108185107

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 2.108185107 and -2.108185107.


Subproblem 1
x + 0.6666666665 = 2.108185107

Simplifying
x + 0.6666666665 = 2.108185107

Reorder the terms:
0.6666666665 + x = 2.108185107

Solving
0.6666666665 + x = 2.108185107

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 = 2.108185107 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 2.108185107 + -0.6666666665
x = 2.108185107 + -0.6666666665

Combine like terms: 2.108185107 + -0.6666666665 = 1.4415184405
x = 1.4415184405

Simplifying
x = 1.4415184405


Subproblem 2
x + 0.6666666665 = -2.108185107

Simplifying
x + 0.6666666665 = -2.108185107

Reorder the terms:
0.6666666665 + x = -2.108185107

Solving
0.6666666665 + x = -2.108185107

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 = -2.108185107 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -2.108185107 + -0.6666666665
x = -2.108185107 + -0.6666666665

Combine like terms: -2.108185107 + -0.6666666665 = -2.7748517735
x = -2.7748517735

Simplifying
x = -2.7748517735


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4415184405, -2.7748517735}

See similar equations:

| 6y=11-5y | | 16x^4-10x^2+1=0 | | 2x-4+3x=21 | | 6x-9=3x+9 | | 24-3x=-27 | | ns+8=38 | | 5(x+2)-2(3x-1)=13 | | -12x-11=13 | | 3x-8=x+40 | | 2x-20=x+8 | | w+18=-4 | | -4+b=-5 | | 5x+6=-3+8x-9 | | 5x+6=3+8x-9 | | a+3=10 | | 0=-6r-6r | | -18=2p-5p | | 5x-6=-3+8x-9 | | 1+n-3n=3 | | -2x+5x=-9 | | 0=-4x+5x | | 2(4-2x+y)-4(5+x-y)= | | 3x+2x=-10 | | 1-4b-6=-9 | | 75=35+0.8x | | 5=3x+5+6x | | 0=-n+3n | | 5+2p-5=8 | | 5x-6+3x=-6-8 | | 18=-5x-4x | | 12.99D+14.24D^2=12.825 | | a-6-6a=4 |

Equations solver categories