3x^2-9x-6=0

Simple and best practice solution for 3x^2-9x-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^2-9x-6=0 equation: 


Simplifying
3x2 + -9x + -6 = 0

Reorder the terms:
-6 + -9x + 3x2 = 0

Solving
-6 + -9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -3x + x2 = 0

Solving
-2 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3x + x2 = 0 + 2

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

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

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 = 2 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3x + x2 = 4.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + -1.5 = 2.061552813

Simplifying
x + -1.5 = 2.061552813

Reorder the terms:
-1.5 + x = 2.061552813

Solving
-1.5 + x = 2.061552813

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 = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.061552813 + 1.5
x = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
x = 3.561552813

Simplifying
x = 3.561552813


Subproblem 2
x + -1.5 = -2.061552813

Simplifying
x + -1.5 = -2.061552813

Reorder the terms:
-1.5 + x = -2.061552813

Solving
-1.5 + x = -2.061552813

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 = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.061552813 + 1.5
x = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
x = -0.561552813

Simplifying
x = -0.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.561552813, -0.561552813}
Solution
x = {3.561552813, -0.561552813}

See similar equations:

| -6y+18=9(y+7) | | 12+x=13 | | 7x+3+5x^2=0 | | 3(y-6)=6 | | -10p+9p=1 | | 6x-y=8 | | w^4+4w^2-100=0 | | 3x^2=-x+3 | | 4x^2-34x+42=0 | | (4x+8)+(4x+8)+(6x-4)= | | C^2=8c+24 | | 4x+8+4x+8+6x-4= | | 15x^2-165x=630 | | 3x^2-18x-48=0 | | 5(2x+7)=3(4x-5) | | 55*5.22=x | | 1305/250=c | | 2x^2-2-3x=0 | | 2*5=x | | 3m-24=-5 | | y^2-10y=-25 | | 0.3(x+80)+0.1x=28 | | 2x^4+3x^2=2 | | 6j+1.9=5.5 | | B=A-BC | | x^2+8x=180 | | A=B+BC | | x^2-9x=18 | | 2x^2+6x=-3 | | 7x+5y=74 | | 3x+10y=15x+6y | | 3(5x+1)=-12 |

Equations solver categories