x2-45=580

Solution for x2-45=580 equation:

x2-45=580

We move all terms to the left:

x2-45-(580)=0

We add all the numbers together, and all the variables

x^2-625=0

a = 1; b = 0; c = -625;
Δ = b2-4ac
Δ = 02-4·1·(-625)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50}{2*1}=\frac{-50}{2}
=-25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50}{2*1}=\frac{50}{2}
=25
$