x^2=(53)2+(5)

Solution for x^2=(53)2+(5) equation:

x^2=(53)2+(5)

We move all terms to the left:

x^2-((53)2+(5))=0

We add all the numbers together, and all the variables

x^2-537=0

a = 1; b = 0; c = -537;
Δ = b2-4ac
Δ = 02-4·1·(-537)
Δ = 2148
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:

$\sqrt{\Delta}=\sqrt{2148}=\sqrt{4*537}=\sqrt{4}*\sqrt{537}=2\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{537}}{2*1}=\frac{0-2\sqrt{537}}{2}
=-\frac{2\sqrt{537}}{2}
=-\sqrt{537}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{537}}{2*1}=\frac{0+2\sqrt{537}}{2}
=\frac{2\sqrt{537}}{2}
=\sqrt{537}
$