5y(y-3)=3-y

Solution for 5y(y-3)=3-y equation:

5y(y-3)=3-y

We move all terms to the left:

5y(y-3)-(3-y)=0

We add all the numbers together, and all the variables

5y(y-3)-(-1y+3)=0

We multiply parentheses

5y^2-15y-(-1y+3)=0

We get rid of parentheses

5y^2-15y+1y-3=0

We add all the numbers together, and all the variables

5y^2-14y-3=0

a = 5; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·5·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*5}=\frac{-2}{10}
=-1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*5}=\frac{30}{10}
=3
$