(a-8)(7a-8)=10

Solution for (a-8)(7a-8)=10 equation:

(a-8)(7a-8)=10

We move all terms to the left:

(a-8)(7a-8)-(10)=0

We multiply parentheses ..

(+7a^2-8a-56a+64)-10=0

We get rid of parentheses

7a^2-8a-56a+64-10=0

We add all the numbers together, and all the variables

7a^2-64a+54=0

a = 7; b = -64; c = +54;
Δ = b2-4ac
Δ = -642-4·7·54
Δ = 2584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2584}=\sqrt{4*646}=\sqrt{4}*\sqrt{646}=2\sqrt{646}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{646}}{2*7}=\frac{64-2\sqrt{646}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{646}}{2*7}=\frac{64+2\sqrt{646}}{14}
$