8x(x-8)=x+2

Solution for 8x(x-8)=x+2 equation:

8x(x-8)=x+2

We move all terms to the left:

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

We multiply parentheses

8x^2-64x-(x+2)=0

We get rid of parentheses

8x^2-64x-x-2=0

We add all the numbers together, and all the variables

8x^2-65x-2=0

a = 8; b = -65; c = -2;
Δ = b2-4ac
Δ = -652-4·8·(-2)
Δ = 4289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{4289}}{2*8}=\frac{65-\sqrt{4289}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4289}}{2*8}=\frac{65+\sqrt{4289}}{16}
$