11=121/x^2,

Solution for 11=121/x^2, equation:

11=121/x^2.

We move all terms to the left:

11-(121/x^2.)=0


Domain of the equation: x^2.)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-121/x^2.+11=0

We multiply all the terms by the denominator


11*x^2.-121=0

Wy multiply elements

11x^2-121=0

a = 11; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·11·(-121)
Δ = 5324
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:

$\sqrt{\Delta}=\sqrt{5324}=\sqrt{484*11}=\sqrt{484}*\sqrt{11}=22\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{11}}{2*11}=\frac{0-22\sqrt{11}}{22}
=-\frac{22\sqrt{11}}{22}
=-\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{11}}{2*11}=\frac{0+22\sqrt{11}}{22}
=\frac{22\sqrt{11}}{22}
=\sqrt{11}
$