(x-15)(x+5)=90

Solution for (x-15)(x+5)=90 equation:

(x-15)(x+5)=90

We move all terms to the left:

(x-15)(x+5)-(90)=0

We multiply parentheses ..

(+x^2+5x-15x-75)-90=0

We get rid of parentheses

x^2+5x-15x-75-90=0

We add all the numbers together, and all the variables

x^2-10x-165=0

a = 1; b = -10; c = -165;
Δ = b2-4ac
Δ = -102-4·1·(-165)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{190}}{2*1}=\frac{10-2\sqrt{190}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{190}}{2*1}=\frac{10+2\sqrt{190}}{2}
$