(6x-27)(5x-5)=180

Solution for (6x-27)(5x-5)=180 equation:

(6x-27)(5x-5)=180

We move all terms to the left:

(6x-27)(5x-5)-(180)=0

We multiply parentheses ..

(+30x^2-30x-135x+135)-180=0

We get rid of parentheses

30x^2-30x-135x+135-180=0

We add all the numbers together, and all the variables

30x^2-165x-45=0

a = 30; b = -165; c = -45;
Δ = b2-4ac
Δ = -1652-4·30·(-45)
Δ = 32625
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:

$\sqrt{\Delta}=\sqrt{32625}=\sqrt{225*145}=\sqrt{225}*\sqrt{145}=15\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-15\sqrt{145}}{2*30}=\frac{165-15\sqrt{145}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+15\sqrt{145}}{2*30}=\frac{165+15\sqrt{145}}{60}
$