11a^2=9

Solution for 11a^2=9 equation:

11a^2=9

We move all terms to the left:

11a^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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$a_{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}
$
$a_{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}
$