2250^2=2000^2+b^2

Solution for 2250^2=2000^2+b^2 equation:

2250^2=2000^2+b^2

We move all terms to the left:

2250^2-(2000^2+b^2)=0

We add all the numbers together, and all the variables

-(2000^2+b^2)+5062500=0

We get rid of parentheses

-b^2+5062500-2000^2=0

We add all the numbers together, and all the variables

-1b^2+1062500=0

a = -1; b = 0; c = +1062500;
Δ = b2-4ac
Δ = 02-4·(-1)·1062500
Δ = 4250000
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:

$\sqrt{\Delta}=\sqrt{4250000}=\sqrt{250000*17}=\sqrt{250000}*\sqrt{17}=500\sqrt{17}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-500\sqrt{17}}{2*-1}=\frac{0-500\sqrt{17}}{-2}
=-\frac{500\sqrt{17}}{-2}
=-\frac{250\sqrt{17}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+500\sqrt{17}}{2*-1}=\frac{0+500\sqrt{17}}{-2}
=\frac{500\sqrt{17}}{-2}
=\frac{250\sqrt{17}}{-1}
$