(4x+20)(9x+4)=180

Solution for (4x+20)(9x+4)=180 equation:

(4x+20)(9x+4)=180

We move all terms to the left:

(4x+20)(9x+4)-(180)=0

We multiply parentheses ..

(+36x^2+16x+180x+80)-180=0

We get rid of parentheses

36x^2+16x+180x+80-180=0

We add all the numbers together, and all the variables

36x^2+196x-100=0

a = 36; b = 196; c = -100;
Δ = b2-4ac
Δ = 1962-4·36·(-100)
Δ = 52816
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:

$\sqrt{\Delta}=\sqrt{52816}=\sqrt{16*3301}=\sqrt{16}*\sqrt{3301}=4\sqrt{3301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-4\sqrt{3301}}{2*36}=\frac{-196-4\sqrt{3301}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+4\sqrt{3301}}{2*36}=\frac{-196+4\sqrt{3301}}{72}
$