-9y-4=2y^2

Solution for -9y-4=2y^2 equation:

-9y-4=2y^2

We move all terms to the left:

-9y-4-(2y^2)=0

determiningTheFunctionDomain
-2y^2-9y-4=0

a = -2; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·(-2)·(-4)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*-2}=\frac{2}{-4}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*-2}=\frac{16}{-4}
=-4
$