140^2+b^2=400^2

Solution for 140^2+b^2=400^2 equation:

140^2+b^2=400^2

We move all terms to the left:

140^2+b^2-(400^2)=0

We add all the numbers together, and all the variables

b^2-140400=0

a = 1; b = 0; c = -140400;
Δ = b2-4ac
Δ = 02-4·1·(-140400)
Δ = 561600
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:

$\sqrt{\Delta}=\sqrt{561600}=\sqrt{14400*39}=\sqrt{14400}*\sqrt{39}=120\sqrt{39}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{39}}{2*1}=\frac{0-120\sqrt{39}}{2}
=-\frac{120\sqrt{39}}{2}
=-60\sqrt{39}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{39}}{2*1}=\frac{0+120\sqrt{39}}{2}
=\frac{120\sqrt{39}}{2}
=60\sqrt{39}
$