9/11=x^2

Solution for 9/11=x^2 equation:

9/11=x^2

We move all terms to the left:

9/11-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+9/11=0

We multiply all the terms by the denominator


-1x^2*11+9=0

Wy multiply elements

-11x^2+9=0

a = -11; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-11)·9
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{11}}{2*-11}=\frac{0-6\sqrt{11}}{-22}
=-\frac{6\sqrt{11}}{-22}
=-\frac{3\sqrt{11}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{11}}{2*-11}=\frac{0+6\sqrt{11}}{-22}
=\frac{6\sqrt{11}}{-22}
=\frac{3\sqrt{11}}{-11}
$