150^2+300^2=x^2

Solution for 150^2+300^2=x^2 equation:

150^2+300^2=x^2

We move all terms to the left:

150^2+300^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+112500=0

a = -1; b = 0; c = +112500;
Δ = b2-4ac
Δ = 02-4·(-1)·112500
Δ = 450000
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:

$\sqrt{\Delta}=\sqrt{450000}=\sqrt{90000*5}=\sqrt{90000}*\sqrt{5}=300\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{5}}{2*-1}=\frac{0-300\sqrt{5}}{-2}
=-\frac{300\sqrt{5}}{-2}
=-\frac{150\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{5}}{2*-1}=\frac{0+300\sqrt{5}}{-2}
=\frac{300\sqrt{5}}{-2}
=\frac{150\sqrt{5}}{-1}
$