y^2+y^2=65

Solution for y^2+y^2=65 equation:

y^2+y^2=65

We move all terms to the left:

y^2+y^2-(65)=0

We add all the numbers together, and all the variables

2y^2-65=0

a = 2; b = 0; c = -65;
Δ = b2-4ac
Δ = 02-4·2·(-65)
Δ = 520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{130}}{2*2}=\frac{0-2\sqrt{130}}{4}
=-\frac{2\sqrt{130}}{4}
=-\frac{\sqrt{130}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{130}}{2*2}=\frac{0+2\sqrt{130}}{4}
=\frac{2\sqrt{130}}{4}
=\frac{\sqrt{130}}{2}
$