4+2/3y=-8-2y

Solution for 4+2/3y=-8-2y equation:

4+2/3y=-8-2y

We move all terms to the left:

4+2/3y-(-8-2y)=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-(-2y-8)+4=0

We get rid of parentheses

2/3y+2y+8+4=0

We multiply all the terms by the denominator


2y*3y+8*3y+4*3y+2=0

Wy multiply elements

6y^2+24y+12y+2=0

We add all the numbers together, and all the variables

6y^2+36y+2=0

a = 6; b = 36; c = +2;
Δ = b2-4ac
Δ = 362-4·6·2
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{78}}{2*6}=\frac{-36-4\sqrt{78}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{78}}{2*6}=\frac{-36+4\sqrt{78}}{12}
$