15y^2=3-4y

Solution for 15y^2=3-4y equation:

15y^2=3-4y

We move all terms to the left:

15y^2-(3-4y)=0

We add all the numbers together, and all the variables

15y^2-(-4y+3)=0

We get rid of parentheses

15y^2+4y-3=0

a = 15; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·15·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*15}=\frac{-18}{30}
=-3/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*15}=\frac{10}{30}
=1/3
$