(x-3)(x-8)=84

Solution for (x-3)(x-8)=84 equation:

(x-3)(x-8)=84

We move all terms to the left:

(x-3)(x-8)-(84)=0

We multiply parentheses ..

(+x^2-8x-3x+24)-84=0

We get rid of parentheses

x^2-8x-3x+24-84=0

We add all the numbers together, and all the variables

x^2-11x-60=0

a = 1; b = -11; c = -60;
Δ = b2-4ac
Δ = -112-4·1·(-60)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-19}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+19}{2*1}=\frac{30}{2}
=15
$