(a-8)(a-2)=-8

Solution for (a-8)(a-2)=-8 equation:

(a-8)(a-2)=-8

We move all terms to the left:

(a-8)(a-2)-(-8)=0

We add all the numbers together, and all the variables

(a-8)(a-2)+8=0

We multiply parentheses ..

(+a^2-2a-8a+16)+8=0

We get rid of parentheses

a^2-2a-8a+16+8=0

We add all the numbers together, and all the variables

a^2-10a+24=0

a = 1; b = -10; c = +24;
Δ = b2-4ac
Δ = -102-4·1·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*1}=\frac{8}{2}
=4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*1}=\frac{12}{2}
=6
$