2y2+7+61+y2=117

Solution for 2y2+7+61+y2=117 equation:

2y^2+7+61+y2=117

We move all terms to the left:

2y^2+7+61+y2-(117)=0

We add all the numbers together, and all the variables

3y^2-49=0

a = 3; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·3·(-49)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*3}=\frac{0-14\sqrt{3}}{6}
=-\frac{14\sqrt{3}}{6}
=-\frac{7\sqrt{3}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*3}=\frac{0+14\sqrt{3}}{6}
=\frac{14\sqrt{3}}{6}
=\frac{7\sqrt{3}}{3}
$