49^2+x^2=625^2

Solution for 49^2+x^2=625^2 equation:

49^2+x^2=625^2

We move all terms to the left:

49^2+x^2-(625^2)=0

We add all the numbers together, and all the variables

x^2-388224=0

a = 1; b = 0; c = -388224;
Δ = b2-4ac
Δ = 02-4·1·(-388224)
Δ = 1552896
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:

$\sqrt{\Delta}=\sqrt{1552896}=\sqrt{2304*674}=\sqrt{2304}*\sqrt{674}=48\sqrt{674}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{674}}{2*1}=\frac{0-48\sqrt{674}}{2}
=-\frac{48\sqrt{674}}{2}
=-24\sqrt{674}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{674}}{2*1}=\frac{0+48\sqrt{674}}{2}
=\frac{48\sqrt{674}}{2}
=24\sqrt{674}
$