2y+6=1/3y-4

Solution for 2y+6=1/3y-4 equation:

2y+6=1/3y-4

We move all terms to the left:

2y+6-(1/3y-4)=0


Domain of the equation: 3y-4)!=0

y∈R


We get rid of parentheses

2y-1/3y+4+6=0

We multiply all the terms by the denominator


2y*3y+4*3y+6*3y-1=0

Wy multiply elements

6y^2+12y+18y-1=0

We add all the numbers together, and all the variables

6y^2+30y-1=0

a = 6; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·6·(-1)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*6}=\frac{-30-2\sqrt{231}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*6}=\frac{-30+2\sqrt{231}}{12}
$