(5x-15)(20x-5)=180

Solution for (5x-15)(20x-5)=180 equation:

(5x-15)(20x-5)=180

We move all terms to the left:

(5x-15)(20x-5)-(180)=0

We multiply parentheses ..

(+100x^2-25x-300x+75)-180=0

We get rid of parentheses

100x^2-25x-300x+75-180=0

We add all the numbers together, and all the variables

100x^2-325x-105=0

a = 100; b = -325; c = -105;
Δ = b2-4ac
Δ = -3252-4·100·(-105)
Δ = 147625
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:

$\sqrt{\Delta}=\sqrt{147625}=\sqrt{25*5905}=\sqrt{25}*\sqrt{5905}=5\sqrt{5905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-325)-5\sqrt{5905}}{2*100}=\frac{325-5\sqrt{5905}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-325)+5\sqrt{5905}}{2*100}=\frac{325+5\sqrt{5905}}{200}
$