(4x+9)(5x+5)=180

Solution for (4x+9)(5x+5)=180 equation:

(4x+9)(5x+5)=180

We move all terms to the left:

(4x+9)(5x+5)-(180)=0

We multiply parentheses ..

(+20x^2+20x+45x+45)-180=0

We get rid of parentheses

20x^2+20x+45x+45-180=0

We add all the numbers together, and all the variables

20x^2+65x-135=0

a = 20; b = 65; c = -135;
Δ = b2-4ac
Δ = 652-4·20·(-135)
Δ = 15025
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:

$\sqrt{\Delta}=\sqrt{15025}=\sqrt{25*601}=\sqrt{25}*\sqrt{601}=5\sqrt{601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{601}}{2*20}=\frac{-65-5\sqrt{601}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{601}}{2*20}=\frac{-65+5\sqrt{601}}{40}
$