5y^2-2=-9y

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

5y^2-2=-9y

We move all terms to the left:

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