5+6y^2=113

Solution for 5+6y^2=113 equation:

5+6y^2=113

We move all terms to the left:

5+6y^2-(113)=0

We add all the numbers together, and all the variables

6y^2-108=0

a = 6; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·6·(-108)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*6}=\frac{0-36\sqrt{2}}{12}
=-\frac{36\sqrt{2}}{12}
=-3\sqrt{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*6}=\frac{0+36\sqrt{2}}{12}
=\frac{36\sqrt{2}}{12}
=3\sqrt{2}
$