x^2+x^2=1500^2

Solution for x^2+x^2=1500^2 equation:

x^2+x^2=1500^2

We move all terms to the left:

x^2+x^2-(1500^2)=0

We add all the numbers together, and all the variables

2x^2-2250000=0

a = 2; b = 0; c = -2250000;
Δ = b2-4ac
Δ = 02-4·2·(-2250000)
Δ = 18000000
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:

$\sqrt{\Delta}=\sqrt{18000000}=\sqrt{9000000*2}=\sqrt{9000000}*\sqrt{2}=3000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3000\sqrt{2}}{2*2}=\frac{0-3000\sqrt{2}}{4}
=-\frac{3000\sqrt{2}}{4}
=-750\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3000\sqrt{2}}{2*2}=\frac{0+3000\sqrt{2}}{4}
=\frac{3000\sqrt{2}}{4}
=750\sqrt{2}
$