x^2+11^2=38^2

Solution for x^2+11^2=38^2 equation:

x^2+11^2=38^2

We move all terms to the left:

x^2+11^2-(38^2)=0

We add all the numbers together, and all the variables

x^2-1323=0

a = 1; b = 0; c = -1323;
Δ = b2-4ac
Δ = 02-4·1·(-1323)
Δ = 5292
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:

$\sqrt{\Delta}=\sqrt{5292}=\sqrt{1764*3}=\sqrt{1764}*\sqrt{3}=42\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{3}}{2*1}=\frac{0-42\sqrt{3}}{2}
=-\frac{42\sqrt{3}}{2}
=-21\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{3}}{2*1}=\frac{0+42\sqrt{3}}{2}
=\frac{42\sqrt{3}}{2}
=21\sqrt{3}
$