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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-5y+2y-(-3y(y+3))-6=0


We calculate terms in parentheses: -(-3y(y+3)), so:

-3y(y+3)

We multiply parentheses

-3y^2-9y

Back to the equation:

-(-3y^2-9y)


We add all the numbers together, and all the variables

-(-3y^2-9y)-3y-6=0

We get rid of parentheses

3y^2+9y-3y-6=0

We add all the numbers together, and all the variables

3y^2+6y-6=0

a = 3; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·3·(-6)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*3}=\frac{-6-6\sqrt{3}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*3}=\frac{-6+6\sqrt{3}}{6}
$