(X-8)(x-8+x-10)=24

Solution for (X-8)(x-8+x-10)=24 equation:

(X-8)(X-8+X-10)=24

We move all terms to the left:

(X-8)(X-8+X-10)-(24)=0

We add all the numbers together, and all the variables

(X-8)(2X-18)-24=0

We multiply parentheses ..

(+2X^2-18X-16X+144)-24=0

We get rid of parentheses

2X^2-18X-16X+144-24=0

We add all the numbers together, and all the variables

2X^2-34X+120=0

a = 2; b = -34; c = +120;
Δ = b2-4ac
Δ = -342-4·2·120
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-14}{2*2}=\frac{20}{4}
=5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+14}{2*2}=\frac{48}{4}
=12
$