(4x-20)(2x+30)=180

Solution for (4x-20)(2x+30)=180 equation:

(4x-20)(2x+30)=180

We move all terms to the left:

(4x-20)(2x+30)-(180)=0

We multiply parentheses ..

(+8x^2+120x-40x-600)-180=0

We get rid of parentheses

8x^2+120x-40x-600-180=0

We add all the numbers together, and all the variables

8x^2+80x-780=0

a = 8; b = 80; c = -780;
Δ = b2-4ac
Δ = 802-4·8·(-780)
Δ = 31360
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:

$\sqrt{\Delta}=\sqrt{31360}=\sqrt{3136*10}=\sqrt{3136}*\sqrt{10}=56\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-56\sqrt{10}}{2*8}=\frac{-80-56\sqrt{10}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+56\sqrt{10}}{2*8}=\frac{-80+56\sqrt{10}}{16}
$