(x-15)(x+77)=180

Solution for (x-15)(x+77)=180 equation:

(x-15)(x+77)=180

We move all terms to the left:

(x-15)(x+77)-(180)=0

We multiply parentheses ..

(+x^2+77x-15x-1155)-180=0

We get rid of parentheses

x^2+77x-15x-1155-180=0

We add all the numbers together, and all the variables

x^2+62x-1335=0

a = 1; b = 62; c = -1335;
Δ = b2-4ac
Δ = 622-4·1·(-1335)
Δ = 9184
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:

$\sqrt{\Delta}=\sqrt{9184}=\sqrt{16*574}=\sqrt{16}*\sqrt{574}=4\sqrt{574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-4\sqrt{574}}{2*1}=\frac{-62-4\sqrt{574}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+4\sqrt{574}}{2*1}=\frac{-62+4\sqrt{574}}{2}
$