x^2-9x=580

Solution for x^2-9x=580 equation:

x^2-9x=580

We move all terms to the left:

x^2-9x-(580)=0

a = 1; b = -9; c = -580;
Δ = b2-4ac
Δ = -92-4·1·(-580)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-49}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+49}{2*1}=\frac{58}{2}
=29
$