60^2+x^2=61^3

Solution for 60^2+x^2=61^3 equation:

60^2+x^2=61^3

We move all terms to the left:

60^2+x^2-(61^3)=0

We add all the numbers together, and all the variables

x^2-223381=0

a = 1; b = 0; c = -223381;
Δ = b2-4ac
Δ = 02-4·1·(-223381)
Δ = 893524
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:

$\sqrt{\Delta}=\sqrt{893524}=\sqrt{4*223381}=\sqrt{4}*\sqrt{223381}=2\sqrt{223381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{223381}}{2*1}=\frac{0-2\sqrt{223381}}{2}
=-\frac{2\sqrt{223381}}{2}
=-\sqrt{223381}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{223381}}{2*1}=\frac{0+2\sqrt{223381}}{2}
=\frac{2\sqrt{223381}}{2}
=\sqrt{223381}
$