2y+11=1/3y+2

Solution for 2y+11=1/3y+2 equation:

2y+11=1/3y+2

We move all terms to the left:

2y+11-(1/3y+2)=0


Domain of the equation: 3y+2)!=0

y∈R


We get rid of parentheses

2y-1/3y-2+11=0

We multiply all the terms by the denominator


2y*3y-2*3y+11*3y-1=0

Wy multiply elements

6y^2-6y+33y-1=0

We add all the numbers together, and all the variables

6y^2+27y-1=0

a = 6; b = 27; c = -1;
Δ = b2-4ac
Δ = 272-4·6·(-1)
Δ = 753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{753}}{2*6}=\frac{-27-\sqrt{753}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{753}}{2*6}=\frac{-27+\sqrt{753}}{12}
$