(5x-5)(x-1)=72

Solution for (5x-5)(x-1)=72 equation:

(5x-5)(x-1)=72

We move all terms to the left:

(5x-5)(x-1)-(72)=0

We multiply parentheses ..

(+5x^2-5x-5x+5)-72=0

We get rid of parentheses

5x^2-5x-5x+5-72=0

We add all the numbers together, and all the variables

5x^2-10x-67=0

a = 5; b = -10; c = -67;
Δ = b2-4ac
Δ = -102-4·5·(-67)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-12\sqrt{10}}{2*5}=\frac{10-12\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+12\sqrt{10}}{2*5}=\frac{10+12\sqrt{10}}{10}
$