(x-5)(x-8)=88

Solution for (x-5)(x-8)=88 equation:

(x-5)(x-8)=88

We move all terms to the left:

(x-5)(x-8)-(88)=0

We multiply parentheses ..

(+x^2-8x-5x+40)-88=0

We get rid of parentheses

x^2-8x-5x+40-88=0

We add all the numbers together, and all the variables

x^2-13x-48=0

a = 1; b = -13; c = -48;
Δ = b2-4ac
Δ = -132-4·1·(-48)
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{-(-13)-19}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*1}=\frac{32}{2}
=16
$