11y2=15

Solution for 11y2=15 equation:

11y^2=15

We move all terms to the left:

11y^2-(15)=0

a = 11; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·11·(-15)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{165}}{2*11}=\frac{0-2\sqrt{165}}{22}
=-\frac{2\sqrt{165}}{22}
=-\frac{\sqrt{165}}{11}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{165}}{2*11}=\frac{0+2\sqrt{165}}{22}
=\frac{2\sqrt{165}}{22}
=\frac{\sqrt{165}}{11}
$