2500^2=x^2+1666^2

Solution for 2500^2=x^2+1666^2 equation:

2500^2=x^2+1666^2

We move all terms to the left:

2500^2-(x^2+1666^2)=0

We add all the numbers together, and all the variables

-(x^2+1666^2)+6250000=0

We get rid of parentheses

-x^2+6250000-1666^2=0

We add all the numbers together, and all the variables

-1x^2+3474444=0

a = -1; b = 0; c = +3474444;
Δ = b2-4ac
Δ = 02-4·(-1)·3474444
Δ = 13897776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13897776}=\sqrt{16*868611}=\sqrt{16}*\sqrt{868611}=4\sqrt{868611}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{868611}}{2*-1}=\frac{0-4\sqrt{868611}}{-2}
=-\frac{4\sqrt{868611}}{-2}
=-\frac{2\sqrt{868611}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{868611}}{2*-1}=\frac{0+4\sqrt{868611}}{-2}
=\frac{4\sqrt{868611}}{-2}
=\frac{2\sqrt{868611}}{-1}
$