(X-4)(x-8)-5=0

Solution for (X-4)(x-8)-5=0 equation:

(X-4)(X-8)-5=0

We multiply parentheses ..

(+X^2-8X-4X+32)-5=0

We get rid of parentheses

X^2-8X-4X+32-5=0

We add all the numbers together, and all the variables

X^2-12X+27=0

a = 1; b = -12; c = +27;
Δ = b2-4ac
Δ = -122-4·1·27
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6}{2*1}=\frac{6}{2}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6}{2*1}=\frac{18}{2}
=9
$