6y(2y+6)=4(9+3y)

Solution for 6y(2y+6)=4(9+3y) equation:

6y(2y+6)=4(9+3y)

We move all terms to the left:

6y(2y+6)-(4(9+3y))=0

We add all the numbers together, and all the variables

6y(2y+6)-(4(3y+9))=0

We multiply parentheses

12y^2+36y-(4(3y+9))=0


We calculate terms in parentheses: -(4(3y+9)), so:

4(3y+9)

We multiply parentheses

12y+36

Back to the equation:

-(12y+36)


We get rid of parentheses

12y^2+36y-12y-36=0

We add all the numbers together, and all the variables

12y^2+24y-36=0

a = 12; b = 24; c = -36;
Δ = b2-4ac
Δ = 242-4·12·(-36)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-48}{2*12}=\frac{-72}{24}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+48}{2*12}=\frac{24}{24}
=1
$