x^2=22^2+34^2

Solution for x^2=22^2+34^2 equation:

x^2=22^2+34^2

We move all terms to the left:

x^2-(22^2+34^2)=0

We add all the numbers together, and all the variables

x^2-1640=0

a = 1; b = 0; c = -1640;
Δ = b2-4ac
Δ = 02-4·1·(-1640)
Δ = 6560
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:

$\sqrt{\Delta}=\sqrt{6560}=\sqrt{16*410}=\sqrt{16}*\sqrt{410}=4\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{410}}{2*1}=\frac{0-4\sqrt{410}}{2}
=-\frac{4\sqrt{410}}{2}
=-2\sqrt{410}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{410}}{2*1}=\frac{0+4\sqrt{410}}{2}
=\frac{4\sqrt{410}}{2}
=2\sqrt{410}
$