11x^2-22x=11

Solution for 11x^2-22x=11 equation:

11x^2-22x=11

We move all terms to the left:

11x^2-22x-(11)=0

a = 11; b = -22; c = -11;
Δ = b2-4ac
Δ = -222-4·11·(-11)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22\sqrt{2}}{2*11}=\frac{22-22\sqrt{2}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22\sqrt{2}}{2*11}=\frac{22+22\sqrt{2}}{22}
$