a^2-8a=65

Solution for a^2-8a=65 equation:

a^2-8a=65

We move all terms to the left:

a^2-8a-(65)=0

a = 1; b = -8; c = -65;
Δ = b2-4ac
Δ = -82-4·1·(-65)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-18}{2*1}=\frac{-10}{2}
=-5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+18}{2*1}=\frac{26}{2}
=13
$