(2x-2)(3x-7)=25

Solution for (2x-2)(3x-7)=25 equation:

(2x-2)(3x-7)=25

We move all terms to the left:

(2x-2)(3x-7)-(25)=0

We multiply parentheses ..

(+6x^2-14x-6x+14)-25=0

We get rid of parentheses

6x^2-14x-6x+14-25=0

We add all the numbers together, and all the variables

6x^2-20x-11=0

a = 6; b = -20; c = -11;
Δ = b2-4ac
Δ = -202-4·6·(-11)
Δ = 664
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:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{166}}{2*6}=\frac{20-2\sqrt{166}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{166}}{2*6}=\frac{20+2\sqrt{166}}{12}
$