(3x+5)(7x-7)=180

Solution for (3x+5)(7x-7)=180 equation:

(3x+5)(7x-7)=180

We move all terms to the left:

(3x+5)(7x-7)-(180)=0

We multiply parentheses ..

(+21x^2-21x+35x-35)-180=0

We get rid of parentheses

21x^2-21x+35x-35-180=0

We add all the numbers together, and all the variables

21x^2+14x-215=0

a = 21; b = 14; c = -215;
Δ = b2-4ac
Δ = 142-4·21·(-215)
Δ = 18256
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:

$\sqrt{\Delta}=\sqrt{18256}=\sqrt{16*1141}=\sqrt{16}*\sqrt{1141}=4\sqrt{1141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{1141}}{2*21}=\frac{-14-4\sqrt{1141}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{1141}}{2*21}=\frac{-14+4\sqrt{1141}}{42}
$