-9y=5y^2-2

Solution for -9y=5y^2-2 equation:

-9y=5y^2-2

We move all terms to the left:

-9y-(5y^2-2)=0

We get rid of parentheses

-5y^2-9y+2=0

a = -5; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-5)·2
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*-5}=\frac{-2}{-10}
=1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*-5}=\frac{20}{-10}
=-2
$