4y=12y(6-2y)

Solution for 4y=12y(6-2y) equation:

4y=12y(6-2y)

We move all terms to the left:

4y-(12y(6-2y))=0

We add all the numbers together, and all the variables

4y-(12y(-2y+6))=0


We calculate terms in parentheses: -(12y(-2y+6)), so:

12y(-2y+6)

We multiply parentheses

-24y^2+72y

Back to the equation:

-(-24y^2+72y)


We get rid of parentheses

24y^2-72y+4y=0

We add all the numbers together, and all the variables

24y^2-68y=0

a = 24; b = -68; c = 0;
Δ = b2-4ac
Δ = -682-4·24·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-68}{2*24}=\frac{0}{48}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+68}{2*24}=\frac{136}{48}
=2+5/6
$