(X+5)(x-3)=60

Solution for (X+5)(x-3)=60 equation:

(X+5)(X-3)=60

We move all terms to the left:

(X+5)(X-3)-(60)=0

We multiply parentheses ..

(+X^2-3X+5X-15)-60=0

We get rid of parentheses

X^2-3X+5X-15-60=0

We add all the numbers together, and all the variables

X^2+2X-75=0

a = 1; b = 2; c = -75;
Δ = b2-4ac
Δ = 22-4·1·(-75)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{19}}{2*1}=\frac{-2-4\sqrt{19}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{19}}{2*1}=\frac{-2+4\sqrt{19}}{2}
$