15+2x^2=117

Solution for 15+2x^2=117 equation:

15+2x^2=117

We move all terms to the left:

15+2x^2-(117)=0

We add all the numbers together, and all the variables

2x^2-102=0

a = 2; b = 0; c = -102;
Δ = b2-4ac
Δ = 02-4·2·(-102)
Δ = 816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*2}=\frac{0-4\sqrt{51}}{4}
=-\frac{4\sqrt{51}}{4}
=-\sqrt{51}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*2}=\frac{0+4\sqrt{51}}{4}
=\frac{4\sqrt{51}}{4}
=\sqrt{51}
$