150^2+b^2=840^2

Solution for 150^2+b^2=840^2 equation:

150^2+b^2=840^2

We move all terms to the left:

150^2+b^2-(840^2)=0

We add all the numbers together, and all the variables

b^2-683100=0

a = 1; b = 0; c = -683100;
Δ = b2-4ac
Δ = 02-4·1·(-683100)
Δ = 2732400
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:

$\sqrt{\Delta}=\sqrt{2732400}=\sqrt{3600*759}=\sqrt{3600}*\sqrt{759}=60\sqrt{759}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{759}}{2*1}=\frac{0-60\sqrt{759}}{2}
=-\frac{60\sqrt{759}}{2}
=-30\sqrt{759}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{759}}{2*1}=\frac{0+60\sqrt{759}}{2}
=\frac{60\sqrt{759}}{2}
=30\sqrt{759}
$