x^2-59=230

Solution for x^2-59=230 equation:

x^2-59=230

We move all terms to the left:

x^2-59-(230)=0

We add all the numbers together, and all the variables

x^2-289=0

a = 1; b = 0; c = -289;
Δ = b2-4ac
Δ = 02-4·1·(-289)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34}{2*1}=\frac{34}{2}
=17
$