11x^2=75

Solution for 11x^2=75 equation:

11x^2=75

We move all terms to the left:

11x^2-(75)=0

a = 11; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·11·(-75)
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{33}}{2*11}=\frac{0-10\sqrt{33}}{22}
=-\frac{10\sqrt{33}}{22}
=-\frac{5\sqrt{33}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{33}}{2*11}=\frac{0+10\sqrt{33}}{22}
=\frac{10\sqrt{33}}{22}
=\frac{5\sqrt{33}}{11}
$