4x^2+6x-90=0

Simple and best practice solution for 4x^2+6x-90=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 4x^2+6x-90=0 equation: 


Simplifying
4x2 + 6x + -90 = 0

Reorder the terms:
-90 + 6x + 4x2 = 0

Solving
-90 + 6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 3x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-45 + 3x + 2x2 = 0

Solving
-45 + 3x + 2x2 = 0

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

Divide each side by '2'.
-22.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 1.5x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 1.5x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 1.5x + x2 = 0 + 22.5
1.5x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
1.5x + x2 = 22.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 22.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 22.5 + 0.5625

Combine like terms: 22.5 + 0.5625 = 23.0625
0.5625 + 1.5x + x2 = 23.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 23.0625

Calculate the square root of the right side: 4.802343178

Break this problem into two subproblems by setting 
(x + 0.75) equal to 4.802343178 and -4.802343178.


Subproblem 1
x + 0.75 = 4.802343178

Simplifying
x + 0.75 = 4.802343178

Reorder the terms:
0.75 + x = 4.802343178

Solving
0.75 + x = 4.802343178

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 4.802343178 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 4.802343178 + -0.75
x = 4.802343178 + -0.75

Combine like terms: 4.802343178 + -0.75 = 4.052343178
x = 4.052343178

Simplifying
x = 4.052343178


Subproblem 2
x + 0.75 = -4.802343178

Simplifying
x + 0.75 = -4.802343178

Reorder the terms:
0.75 + x = -4.802343178

Solving
0.75 + x = -4.802343178

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -4.802343178 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -4.802343178 + -0.75
x = -4.802343178 + -0.75

Combine like terms: -4.802343178 + -0.75 = -5.552343178
x = -5.552343178

Simplifying
x = -5.552343178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.052343178, -5.552343178}
Solution
x = {4.052343178, -5.552343178}

See similar equations:

| 5x+525=1500 | | 5x+525=0 | | -3(5p+3)-2(5-14p)=3(7+4p) | | -11/21=-10/21 | | 5x+525=525 | | 5-x/x(x-2)= | | 45(1/2)=1/2x-1/2 | | (2x-10)=(65-x) | | 0.5(x+150)=535 | | lnx+3y=2ln(4y-1) | | -9(4b+1)+(37b-9)=0 | | (x-6)(x-4)=4 | | 5-x/x(x-2) | | l^2+24t-3456=0 | | (5y+8)-(6+4y)=10 | | dy/dx(2sinx) | | 14=2g | | 3y+lnX=2ln(4y-1) | | f(x)=10x^3+10x | | 5e+-7=26 | | t^2+19.7t-208=0 | | 1/3(-1/6)-4 | | 5e+-7=-10 | | 5.2q-5.8-5.5q=-1.3q-5.2 | | 3cos^2x+14cosx-5=0 | | -392x^2+196=0 | | (-2/3)^3(1/8-1/2)-2/3(1/8) | | 5/x=20/14 | | -16t^2+20t+14=0 | | coshx=1 | | 3X+14+3X+10= | | 10n=1.1 |

Equations solver categories