144^2+b^2=225^2

Solution for 144^2+b^2=225^2 equation:

144^2+b^2=225^2

We move all terms to the left:

144^2+b^2-(225^2)=0

We add all the numbers together, and all the variables

b^2-29889=0

a = 1; b = 0; c = -29889;
Δ = b2-4ac
Δ = 02-4·1·(-29889)
Δ = 119556
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:

$\sqrt{\Delta}=\sqrt{119556}=\sqrt{2916*41}=\sqrt{2916}*\sqrt{41}=54\sqrt{41}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{41}}{2*1}=\frac{0-54\sqrt{41}}{2}
=-\frac{54\sqrt{41}}{2}
=-27\sqrt{41}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{41}}{2*1}=\frac{0+54\sqrt{41}}{2}
=\frac{54\sqrt{41}}{2}
=27\sqrt{41}
$