4y^2+4=-9y

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

4y^2+4=-9y

We move all terms to the left:

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

We get rid of parentheses

4y^2+9y+4=0

a = 4; b = 9; c = +4;
Δ = b2-4ac
Δ = 92-4·4·4
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{17}}{2*4}=\frac{-9-\sqrt{17}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{17}}{2*4}=\frac{-9+\sqrt{17}}{8}
$