5^2+b^2=10^2

Solution for 5^2+b^2=10^2 equation:

5^2+b^2=10^2

We move all terms to the left:

5^2+b^2-(10^2)=0

We add all the numbers together, and all the variables

b^2-75=0

a = 1; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·1·(-75)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*1}=\frac{0-10\sqrt{3}}{2}
=-\frac{10\sqrt{3}}{2}
=-5\sqrt{3}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*1}=\frac{0+10\sqrt{3}}{2}
=\frac{10\sqrt{3}}{2}
=5\sqrt{3}
$