(x-3)(x+5)=84

Solution for (x-3)(x+5)=84 equation:

(X-3)(X+5)=84

We move all terms to the left:

(X-3)(X+5)-(84)=0

We multiply parentheses ..

(+X^2+5X-3X-15)-84=0

We get rid of parentheses

X^2+5X-3X-15-84=0

We add all the numbers together, and all the variables

X^2+2X-99=0

a = 1; b = 2; c = -99;
Δ = b2-4ac
Δ = 22-4·1·(-99)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-20}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+20}{2*1}=\frac{18}{2}
=9
$