9y=11y^2-2

Solution for 9y=11y^2-2 equation:

9y=11y^2-2

We move all terms to the left:

9y-(11y^2-2)=0

We get rid of parentheses

-11y^2+9y+2=0

a = -11; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-11)·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-13}{2*-11}=\frac{-22}{-22}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+13}{2*-11}=\frac{4}{-22}
=-2/11
$