(5x+5)(7x-7)=180

Solution for (5x+5)(7x-7)=180 equation:

(5x+5)(7x-7)=180

We move all terms to the left:

(5x+5)(7x-7)-(180)=0

We multiply parentheses ..

(+35x^2-35x+35x-35)-180=0

We get rid of parentheses

35x^2-35x+35x-35-180=0

We add all the numbers together, and all the variables

35x^2-215=0

a = 35; b = 0; c = -215;
Δ = b2-4ac
Δ = 02-4·35·(-215)
Δ = 30100
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:

$\sqrt{\Delta}=\sqrt{30100}=\sqrt{100*301}=\sqrt{100}*\sqrt{301}=10\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{301}}{2*35}=\frac{0-10\sqrt{301}}{70}
=-\frac{10\sqrt{301}}{70}
=-\frac{\sqrt{301}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{301}}{2*35}=\frac{0+10\sqrt{301}}{70}
=\frac{10\sqrt{301}}{70}
=\frac{\sqrt{301}}{7}
$