5y+3y(2+y)=54

Solution for 5y+3y(2+y)=54 equation:

5y+3y(2+y)=54

We move all terms to the left:

5y+3y(2+y)-(54)=0

We add all the numbers together, and all the variables

5y+3y(y+2)-54=0

We multiply parentheses

3y^2+5y+6y-54=0

We add all the numbers together, and all the variables

3y^2+11y-54=0

a = 3; b = 11; c = -54;
Δ = b2-4ac
Δ = 112-4·3·(-54)
Δ = 769
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{-(11)-\sqrt{769}}{2*3}=\frac{-11-\sqrt{769}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{769}}{2*3}=\frac{-11+\sqrt{769}}{6}
$