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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

x^2-5x+3x-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}
$