(x-8)x=598

Solution for (x-8)x=598 equation:

(x-8)x=598

We move all terms to the left:

(x-8)x-(598)=0

We multiply parentheses

x^2-8x-598=0

a = 1; b = -8; c = -598;
Δ = b2-4ac
Δ = -82-4·1·(-598)
Δ = 2456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2456}=\sqrt{4*614}=\sqrt{4}*\sqrt{614}=2\sqrt{614}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{614}}{2*1}=\frac{8-2\sqrt{614}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{614}}{2*1}=\frac{8+2\sqrt{614}}{2}
$