(9x-5)(6x+20)=180

Solution for (9x-5)(6x+20)=180 equation:

(9x-5)(6x+20)=180

We move all terms to the left:

(9x-5)(6x+20)-(180)=0

We multiply parentheses ..

(+54x^2+180x-30x-100)-180=0

We get rid of parentheses

54x^2+180x-30x-100-180=0

We add all the numbers together, and all the variables

54x^2+150x-280=0

a = 54; b = 150; c = -280;
Δ = b2-4ac
Δ = 1502-4·54·(-280)
Δ = 82980
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:

$\sqrt{\Delta}=\sqrt{82980}=\sqrt{36*2305}=\sqrt{36}*\sqrt{2305}=6\sqrt{2305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-6\sqrt{2305}}{2*54}=\frac{-150-6\sqrt{2305}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+6\sqrt{2305}}{2*54}=\frac{-150+6\sqrt{2305}}{108}
$