x^2+300^2=600^2

Solution for x^2+300^2=600^2 equation:

x^2+300^2=600^2

We move all terms to the left:

x^2+300^2-(600^2)=0

We add all the numbers together, and all the variables

x^2-270000=0

a = 1; b = 0; c = -270000;
Δ = b2-4ac
Δ = 02-4·1·(-270000)
Δ = 1080000
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:

$\sqrt{\Delta}=\sqrt{1080000}=\sqrt{360000*3}=\sqrt{360000}*\sqrt{3}=600\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{3}}{2*1}=\frac{0-600\sqrt{3}}{2}
=-\frac{600\sqrt{3}}{2}
=-300\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{3}}{2*1}=\frac{0+600\sqrt{3}}{2}
=\frac{600\sqrt{3}}{2}
=300\sqrt{3}
$