5x(x-8)=x+8

Solution for 5x(x-8)=x+8 equation:

5x(x-8)=x+8

We move all terms to the left:

5x(x-8)-(x+8)=0

We multiply parentheses

5x^2-40x-(x+8)=0

We get rid of parentheses

5x^2-40x-x-8=0

We add all the numbers together, and all the variables

5x^2-41x-8=0

a = 5; b = -41; c = -8;
Δ = b2-4ac
Δ = -412-4·5·(-8)
Δ = 1841
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{-(-41)-\sqrt{1841}}{2*5}=\frac{41-\sqrt{1841}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{1841}}{2*5}=\frac{41+\sqrt{1841}}{10}
$