11x^2=24

Solution for 11x^2=24 equation:

11x^2=24

We move all terms to the left:

11x^2-(24)=0

a = 11; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·11·(-24)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{66}}{2*11}=\frac{0-4\sqrt{66}}{22}
=-\frac{4\sqrt{66}}{22}
=-\frac{2\sqrt{66}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{66}}{2*11}=\frac{0+4\sqrt{66}}{22}
=\frac{4\sqrt{66}}{22}
=\frac{2\sqrt{66}}{11}
$