5y^2+y^2=52

Solution for 5y^2+y^2=52 equation:

5y^2+y^2=52

We move all terms to the left:

5y^2+y^2-(52)=0

We add all the numbers together, and all the variables

6y^2-52=0

a = 6; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·6·(-52)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{78}}{2*6}=\frac{0-4\sqrt{78}}{12}
=-\frac{4\sqrt{78}}{12}
=-\frac{\sqrt{78}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{78}}{2*6}=\frac{0+4\sqrt{78}}{12}
=\frac{4\sqrt{78}}{12}
=\frac{\sqrt{78}}{3}
$