3x^2-4x-45=0

Simple and best practice solution for 3x^2-4x-45=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-45=0 equation: 


Simplifying
3x2 + -4x + -45 = 0

Reorder the terms:
-45 + -4x + 3x2 = 0

Solving
-45 + -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'.
-15 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -1.333333333x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -1.333333333x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1.333333333x + x2 = 0 + 15
-1.333333333x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-1.333333333x + x2 = 15

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 = 15 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 15 + 0.4444444442

Combine like terms: 15 + 0.4444444442 = 15.4444444442
0.4444444442 + -1.333333333x + x2 = 15.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 15.4444444442

Calculate the square root of the right side: 3.929942041

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 3.929942041 and -3.929942041.


Subproblem 1
x + -0.6666666665 = 3.929942041

Simplifying
x + -0.6666666665 = 3.929942041

Reorder the terms:
-0.6666666665 + x = 3.929942041

Solving
-0.6666666665 + x = 3.929942041

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 = 3.929942041 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 3.929942041 + 0.6666666665
x = 3.929942041 + 0.6666666665

Combine like terms: 3.929942041 + 0.6666666665 = 4.5966087075
x = 4.5966087075

Simplifying
x = 4.5966087075


Subproblem 2
x + -0.6666666665 = -3.929942041

Simplifying
x + -0.6666666665 = -3.929942041

Reorder the terms:
-0.6666666665 + x = -3.929942041

Solving
-0.6666666665 + x = -3.929942041

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 = -3.929942041 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -3.929942041 + 0.6666666665
x = -3.929942041 + 0.6666666665

Combine like terms: -3.929942041 + 0.6666666665 = -3.2632753745
x = -3.2632753745

Simplifying
x = -3.2632753745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5966087075, -3.2632753745}

See similar equations:

| m^2(18m+15)=7m | | 4x^2-8=8x | | 12x^2+5x-25=0 | | -5-7(8n-2)=-159 | | 7x(x-5)=0 | | (12a+7)(5a-15)=0 | | (4+v)(4v-7)=0 | | 5x^2=-26x-5 | | 20r=80 | | 5x^2=-11x-2 | | 49=7m | | 3x+7=2x-11 | | -8-5(-5b+2)=-193 | | 15p=450 | | 6x^2+23x+7=0 | | (10x-4)(2x+3)=0 | | 84=6v | | 4v=28 | | 10r^2+43r-9=0 | | (x-8)(8x+1)=0 | | -7(n+8)-8=-92 | | x^2+1=26 | | 500x=150x+2 | | 12x+5-5x=11 | | 2(2x-15)=-20 | | 5-18=3y-2y+1 | | (5x-2)(2x-1)=0 | | -5(1-4x)-2=153 | | -8-5x+6=-18x+12-5x | | 8x-21=2(x-3) | | 18n^2-3n-15=0 | | 11x+3-2x=3x-8 |

Equations solver categories