137^2=105^2+b^2

Solution for 137^2=105^2+b^2 equation:

137^2=105^2+b^2

We move all terms to the left:

137^2-(105^2+b^2)=0

We add all the numbers together, and all the variables

-(105^2+b^2)+18769=0

We get rid of parentheses

-b^2+18769-105^2=0

We add all the numbers together, and all the variables

-1b^2+7744=0

a = -1; b = 0; c = +7744;
Δ = b2-4ac
Δ = 02-4·(-1)·7744
Δ = 30976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30976}=176$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-176}{2*-1}=\frac{-176}{-2}
=+88
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+176}{2*-1}=\frac{176}{-2}
=-88
$