(x-15)(x+77)=90

Solution for (x-15)(x+77)=90 equation:

(x-15)(x+77)=90

We move all terms to the left:

(x-15)(x+77)-(90)=0

We multiply parentheses ..

(+x^2+77x-15x-1155)-90=0

We get rid of parentheses

x^2+77x-15x-1155-90=0

We add all the numbers together, and all the variables

x^2+62x-1245=0

a = 1; b = 62; c = -1245;
Δ = b2-4ac
Δ = 622-4·1·(-1245)
Δ = 8824
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:

$\sqrt{\Delta}=\sqrt{8824}=\sqrt{4*2206}=\sqrt{4}*\sqrt{2206}=2\sqrt{2206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{2206}}{2*1}=\frac{-62-2\sqrt{2206}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{2206}}{2*1}=\frac{-62+2\sqrt{2206}}{2}
$