(4x-5)(2x+20)=180

Solution for (4x-5)(2x+20)=180 equation:

(4x-5)(2x+20)=180

We move all terms to the left:

(4x-5)(2x+20)-(180)=0

We multiply parentheses ..

(+8x^2+80x-10x-100)-180=0

We get rid of parentheses

8x^2+80x-10x-100-180=0

We add all the numbers together, and all the variables

8x^2+70x-280=0

a = 8; b = 70; c = -280;
Δ = b2-4ac
Δ = 702-4·8·(-280)
Δ = 13860
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:

$\sqrt{\Delta}=\sqrt{13860}=\sqrt{36*385}=\sqrt{36}*\sqrt{385}=6\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-6\sqrt{385}}{2*8}=\frac{-70-6\sqrt{385}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+6\sqrt{385}}{2*8}=\frac{-70+6\sqrt{385}}{16}
$