(2x+4)(2x-9)+x=180

Solution for (2x+4)(2x-9)+x=180 equation:

(2x+4)(2x-9)+x=180

We move all terms to the left:

(2x+4)(2x-9)+x-(180)=0

We add all the numbers together, and all the variables

x+(2x+4)(2x-9)-180=0

We multiply parentheses ..

(+4x^2-18x+8x-36)+x-180=0

We get rid of parentheses

4x^2-18x+8x+x-36-180=0

We add all the numbers together, and all the variables

4x^2-9x-216=0

a = 4; b = -9; c = -216;
Δ = b2-4ac
Δ = -92-4·4·(-216)
Δ = 3537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3537}=\sqrt{9*393}=\sqrt{9}*\sqrt{393}=3\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{393}}{2*4}=\frac{9-3\sqrt{393}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{393}}{2*4}=\frac{9+3\sqrt{393}}{8}
$