9y+3y(y-6)=30

Solution for 9y+3y(y-6)=30 equation:

9y+3y(y-6)=30

We move all terms to the left:

9y+3y(y-6)-(30)=0

We multiply parentheses

3y^2+9y-18y-30=0

We add all the numbers together, and all the variables

3y^2-9y-30=0

a = 3; b = -9; c = -30;
Δ = b2-4ac
Δ = -92-4·3·(-30)
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{-(-9)-21}{2*3}=\frac{-12}{6}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*3}=\frac{30}{6}
=5
$