10^2+b^2=24^2

Solution for 10^2+b^2=24^2 equation:

10^2+b^2=24^2

We move all terms to the left:

10^2+b^2-(24^2)=0

We add all the numbers together, and all the variables

b^2-476=0

a = 1; b = 0; c = -476;
Δ = b2-4ac
Δ = 02-4·1·(-476)
Δ = 1904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1904}=\sqrt{16*119}=\sqrt{16}*\sqrt{119}=4\sqrt{119}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{119}}{2*1}=\frac{0-4\sqrt{119}}{2}
=-\frac{4\sqrt{119}}{2}
=-2\sqrt{119}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{119}}{2*1}=\frac{0+4\sqrt{119}}{2}
=\frac{4\sqrt{119}}{2}
=2\sqrt{119}
$