y^2+y^2=288

Solution for y^2+y^2=288 equation:

y^2+y^2=288

We move all terms to the left:

y^2+y^2-(288)=0

We add all the numbers together, and all the variables

2y^2-288=0

a = 2; b = 0; c = -288;
Δ = b2-4ac
Δ = 02-4·2·(-288)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*2}=\frac{-48}{4}
=-12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*2}=\frac{48}{4}
=12
$