5y(y+2)=4-9y

Solution for 5y(y+2)=4-9y equation:

5y(y+2)=4-9y

We move all terms to the left:

5y(y+2)-(4-9y)=0

We add all the numbers together, and all the variables

5y(y+2)-(-9y+4)=0

We multiply parentheses

5y^2+10y-(-9y+4)=0

We get rid of parentheses

5y^2+10y+9y-4=0

We add all the numbers together, and all the variables

5y^2+19y-4=0

a = 5; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·5·(-4)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-21}{2*5}=\frac{-40}{10}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+21}{2*5}=\frac{2}{10}
=1/5
$