(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^2-8x-39=0

a = 6; b = -8; c = -39;
Δ = b2-4ac
Δ = -82-4·6·(-39)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10\sqrt{10}}{2*6}=\frac{8-10\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10\sqrt{10}}{2*6}=\frac{8+10\sqrt{10}}{12}
$