2y^2+14=102

Solution for 2y^2+14=102 equation:

2y^2+14=102

We move all terms to the left:

2y^2+14-(102)=0

We add all the numbers together, and all the variables

2y^2-88=0

a = 2; b = 0; c = -88;
Δ = b2-4ac
Δ = 02-4·2·(-88)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*2}=\frac{0-8\sqrt{11}}{4}
=-\frac{8\sqrt{11}}{4}
=-2\sqrt{11}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*2}=\frac{0+8\sqrt{11}}{4}
=\frac{8\sqrt{11}}{4}
=2\sqrt{11}
$