-1/3y+4y=3

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

-1/3y+4y=3

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

4y-1/3y-3=0

We multiply all the terms by the denominator


4y*3y-3*3y-1=0

Wy multiply elements

12y^2-9y-1=0

a = 12; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·12·(-1)
Δ = 129
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{-(-9)-\sqrt{129}}{2*12}=\frac{9-\sqrt{129}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*12}=\frac{9+\sqrt{129}}{24}
$