9y=5y2-2

Solution for 9y=5y2-2 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{-20}{-10}
=+2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*-5}=\frac{2}{-10}
=-1/5
$