(2x+5)(2x+17)+90=180

Solution for (2x+5)(2x+17)+90=180 equation:

(2x+5)(2x+17)+90=180

We move all terms to the left:

(2x+5)(2x+17)+90-(180)=0

We add all the numbers together, and all the variables

(2x+5)(2x+17)-90=0

We multiply parentheses ..

(+4x^2+34x+10x+85)-90=0

We get rid of parentheses

4x^2+34x+10x+85-90=0

We add all the numbers together, and all the variables

4x^2+44x-5=0

a = 4; b = 44; c = -5;
Δ = b2-4ac
Δ = 442-4·4·(-5)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-12\sqrt{14}}{2*4}=\frac{-44-12\sqrt{14}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+12\sqrt{14}}{2*4}=\frac{-44+12\sqrt{14}}{8}
$