x^2=-68x+580

Solution for x^2=-68x+580 equation:

x^2=-68x+580

We move all terms to the left:

x^2-(-68x+580)=0

We get rid of parentheses

x^2+68x-580=0

a = 1; b = 68; c = -580;
Δ = b2-4ac
Δ = 682-4·1·(-580)
Δ = 6944
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:

$\sqrt{\Delta}=\sqrt{6944}=\sqrt{16*434}=\sqrt{16}*\sqrt{434}=4\sqrt{434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{434}}{2*1}=\frac{-68-4\sqrt{434}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{434}}{2*1}=\frac{-68+4\sqrt{434}}{2}
$