1/3y-2=4y

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

1/3y-2=4y

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -12; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-12)·1
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-12}=\frac{6-2\sqrt{21}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-12}=\frac{6+2\sqrt{21}}{-24}
$