11x^2=3

Solution for 11x^2=3 equation:

11x^2=3

We move all terms to the left:

11x^2-(3)=0

a = 11; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·11·(-3)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{33}}{2*11}=\frac{0-2\sqrt{33}}{22}
=-\frac{2\sqrt{33}}{22}
=-\frac{\sqrt{33}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{33}}{2*11}=\frac{0+2\sqrt{33}}{22}
=\frac{2\sqrt{33}}{22}
=\frac{\sqrt{33}}{11}
$