(X+3)(x-5)=65

Solution for (X+3)(x-5)=65 equation:

(X+3)(X-5)=65

We move all terms to the left:

(X+3)(X-5)-(65)=0

We multiply parentheses ..

(+X^2-5X+3X-15)-65=0

We get rid of parentheses

X^2-5X+3X-15-65=0

We add all the numbers together, and all the variables

X^2-2X-80=0

a = 1; b = -2; c = -80;
Δ = b2-4ac
Δ = -22-4·1·(-80)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*1}=\frac{20}{2}
=10
$