45^2+x^2=83^2

Solution for 45^2+x^2=83^2 equation:

45^2+x^2=83^2

We move all terms to the left:

45^2+x^2-(83^2)=0

We add all the numbers together, and all the variables

x^2-4864=0

a = 1; b = 0; c = -4864;
Δ = b2-4ac
Δ = 02-4·1·(-4864)
Δ = 19456
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:

$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{19}}{2*1}=\frac{0-32\sqrt{19}}{2}
=-\frac{32\sqrt{19}}{2}
=-16\sqrt{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{19}}{2*1}=\frac{0+32\sqrt{19}}{2}
=\frac{32\sqrt{19}}{2}
=16\sqrt{19}
$