(2x+5)(2x+8)=180

Solution for (2x+5)(2x+8)=180 equation:

(2x+5)(2x+8)=180

We move all terms to the left:

(2x+5)(2x+8)-(180)=0

We multiply parentheses ..

(+4x^2+16x+10x+40)-180=0

We get rid of parentheses

4x^2+16x+10x+40-180=0

We add all the numbers together, and all the variables

4x^2+26x-140=0

a = 4; b = 26; c = -140;
Δ = b2-4ac
Δ = 262-4·4·(-140)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-54}{2*4}=\frac{-80}{8}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+54}{2*4}=\frac{28}{8}
=3+1/2
$