2x(x-8)=x+2

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

2x(x-8)=x+2

We move all terms to the left:

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

We multiply parentheses

2x^2-16x-(x+2)=0

We get rid of parentheses

2x^2-16x-x-2=0

We add all the numbers together, and all the variables

2x^2-17x-2=0

a = 2; b = -17; c = -2;
Δ = b2-4ac
Δ = -172-4·2·(-2)
Δ = 305
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{-(-17)-\sqrt{305}}{2*2}=\frac{17-\sqrt{305}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{305}}{2*2}=\frac{17+\sqrt{305}}{4}
$