30y^2=3-9y

Solution for 30y^2=3-9y equation:

30y^2=3-9y

We move all terms to the left:

30y^2-(3-9y)=0

We add all the numbers together, and all the variables

30y^2-(-9y+3)=0

We get rid of parentheses

30y^2+9y-3=0

a = 30; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·30·(-3)
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*30}=\frac{-30}{60}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*30}=\frac{12}{60}
=1/5
$