24^2+b^2=45^2

Solution for 24^2+b^2=45^2 equation:

24^2+b^2=45^2

We move all terms to the left:

24^2+b^2-(45^2)=0

We add all the numbers together, and all the variables

b^2-1449=0

a = 1; b = 0; c = -1449;
Δ = b2-4ac
Δ = 02-4·1·(-1449)
Δ = 5796
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:

$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{161}}{2*1}=\frac{0-6\sqrt{161}}{2}
=-\frac{6\sqrt{161}}{2}
=-3\sqrt{161}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{161}}{2*1}=\frac{0+6\sqrt{161}}{2}
=\frac{6\sqrt{161}}{2}
=3\sqrt{161}
$