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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

30x^2-130x-80=0

a = 30; b = -130; c = -80;
Δ = b2-4ac
Δ = -1302-4·30·(-80)
Δ = 26500
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:

$\sqrt{\Delta}=\sqrt{26500}=\sqrt{100*265}=\sqrt{100}*\sqrt{265}=10\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-10\sqrt{265}}{2*30}=\frac{130-10\sqrt{265}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+10\sqrt{265}}{2*30}=\frac{130+10\sqrt{265}}{60}
$