2/3y+6(y+4)=-36

Solution for 2/3y+6(y+4)=-36 equation:

2/3y+6(y+4)=-36

We move all terms to the left:

2/3y+6(y+4)-(-36)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y+6(y+4)+36=0

We multiply parentheses

2/3y+6y+24+36=0

We multiply all the terms by the denominator


6y*3y+24*3y+36*3y+2=0

Wy multiply elements

18y^2+72y+108y+2=0

We add all the numbers together, and all the variables

18y^2+180y+2=0

a = 18; b = 180; c = +2;
Δ = b2-4ac
Δ = 1802-4·18·2
Δ = 32256
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:

$\sqrt{\Delta}=\sqrt{32256}=\sqrt{2304*14}=\sqrt{2304}*\sqrt{14}=48\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-48\sqrt{14}}{2*18}=\frac{-180-48\sqrt{14}}{36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+48\sqrt{14}}{2*18}=\frac{-180+48\sqrt{14}}{36}
$