(13x-21)(5x+75)=180

Solution for (13x-21)(5x+75)=180 equation:

(13x-21)(5x+75)=180

We move all terms to the left:

(13x-21)(5x+75)-(180)=0

We multiply parentheses ..

(+65x^2+975x-105x-1575)-180=0

We get rid of parentheses

65x^2+975x-105x-1575-180=0

We add all the numbers together, and all the variables

65x^2+870x-1755=0

a = 65; b = 870; c = -1755;
Δ = b2-4ac
Δ = 8702-4·65·(-1755)
Δ = 1213200
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:

$\sqrt{\Delta}=\sqrt{1213200}=\sqrt{3600*337}=\sqrt{3600}*\sqrt{337}=60\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(870)-60\sqrt{337}}{2*65}=\frac{-870-60\sqrt{337}}{130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(870)+60\sqrt{337}}{2*65}=\frac{-870+60\sqrt{337}}{130}
$