(3x+20)(4x-36)=180

Solution for (3x+20)(4x-36)=180 equation:

(3x+20)(4x-36)=180

We move all terms to the left:

(3x+20)(4x-36)-(180)=0

We multiply parentheses ..

(+12x^2-108x+80x-720)-180=0

We get rid of parentheses

12x^2-108x+80x-720-180=0

We add all the numbers together, and all the variables

12x^2-28x-900=0

a = 12; b = -28; c = -900;
Δ = b2-4ac
Δ = -282-4·12·(-900)
Δ = 43984
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:

$\sqrt{\Delta}=\sqrt{43984}=\sqrt{16*2749}=\sqrt{16}*\sqrt{2749}=4\sqrt{2749}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{2749}}{2*12}=\frac{28-4\sqrt{2749}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{2749}}{2*12}=\frac{28+4\sqrt{2749}}{24}
$