65-x^2=8x

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

65-x^2=8x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2-8x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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