13^2+23^3=x2

Solution for 13^2+23^3=x2 equation:

13^2+23^3=x2

We move all terms to the left:

13^2+23^3-(x2)=0

We add all the numbers together, and all the variables

-1x^2+12336=0

a = -1; b = 0; c = +12336;
Δ = b2-4ac
Δ = 02-4·(-1)·12336
Δ = 49344
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:

$\sqrt{\Delta}=\sqrt{49344}=\sqrt{64*771}=\sqrt{64}*\sqrt{771}=8\sqrt{771}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{771}}{2*-1}=\frac{0-8\sqrt{771}}{-2}
=-\frac{8\sqrt{771}}{-2}
=-\frac{4\sqrt{771}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{771}}{2*-1}=\frac{0+8\sqrt{771}}{-2}
=\frac{8\sqrt{771}}{-2}
=\frac{4\sqrt{771}}{-1}
$