15x^2=11

Solution for 15x^2=11 equation:

15x^2=11

We move all terms to the left:

15x^2-(11)=0

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

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{165}}{2*15}=\frac{0-2\sqrt{165}}{30}
=-\frac{2\sqrt{165}}{30}
=-\frac{\sqrt{165}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{165}}{2*15}=\frac{0+2\sqrt{165}}{30}
=\frac{2\sqrt{165}}{30}
=\frac{\sqrt{165}}{15}
$