60^2-b^2=25^2

Solution for 60^2-b^2=25^2 equation:

60^2-b^2=25^2

We move all terms to the left:

60^2-b^2-(25^2)=0

We add all the numbers together, and all the variables

-1b^2+2975=0

a = -1; b = 0; c = +2975;
Δ = b2-4ac
Δ = 02-4·(-1)·2975
Δ = 11900
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:

$\sqrt{\Delta}=\sqrt{11900}=\sqrt{100*119}=\sqrt{100}*\sqrt{119}=10\sqrt{119}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{119}}{2*-1}=\frac{0-10\sqrt{119}}{-2}
=-\frac{10\sqrt{119}}{-2}
=-\frac{5\sqrt{119}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{119}}{2*-1}=\frac{0+10\sqrt{119}}{-2}
=\frac{10\sqrt{119}}{-2}
=\frac{5\sqrt{119}}{-1}
$