X2+y2=150

Solution for X2+y2=150 equation:

X2+X2=150

We move all terms to the left:

X2+X2-(150)=0

We add all the numbers together, and all the variables

2X^2-150=0

a = 2; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·2·(-150)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*2}=\frac{0-20\sqrt{3}}{4}
=-\frac{20\sqrt{3}}{4}
=-5\sqrt{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*2}=\frac{0+20\sqrt{3}}{4}
=\frac{20\sqrt{3}}{4}
=5\sqrt{3}
$