a^2+25^2=50^2

Solution for a^2+25^2=50^2 equation:

a^2+25^2=50^2

We move all terms to the left:

a^2+25^2-(50^2)=0

We add all the numbers together, and all the variables

a^2-1875=0

a = 1; b = 0; c = -1875;
Δ = b2-4ac
Δ = 02-4·1·(-1875)
Δ = 7500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7500}=\sqrt{2500*3}=\sqrt{2500}*\sqrt{3}=50\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{3}}{2*1}=\frac{0-50\sqrt{3}}{2}
=-\frac{50\sqrt{3}}{2}
=-25\sqrt{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{3}}{2*1}=\frac{0+50\sqrt{3}}{2}
=\frac{50\sqrt{3}}{2}
=25\sqrt{3}
$