x(x-8)=513

Solution for x(x-8)=513 equation:

x(x-8)=513

We move all terms to the left:

x(x-8)-(513)=0

We multiply parentheses

x^2-8x-513=0

a = 1; b = -8; c = -513;
Δ = b2-4ac
Δ = -82-4·1·(-513)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-46}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+46}{2*1}=\frac{54}{2}
=27
$