11x^2=55

Solution for 11x^2=55 equation:

11x^2=55

We move all terms to the left:

11x^2-(55)=0

a = 11; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·11·(-55)
Δ = 2420
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:

$\sqrt{\Delta}=\sqrt{2420}=\sqrt{484*5}=\sqrt{484}*\sqrt{5}=22\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{5}}{2*11}=\frac{0-22\sqrt{5}}{22}
=-\frac{22\sqrt{5}}{22}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{5}}{2*11}=\frac{0+22\sqrt{5}}{22}
=\frac{22\sqrt{5}}{22}
=\sqrt{5}
$