2/3y=4y-1

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

2/3y=4y-1

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

2/3y-4y+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

-12y^2+3y+2=0

a = -12; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-12)·2
Δ = 105
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{-(3)-\sqrt{105}}{2*-12}=\frac{-3-\sqrt{105}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-12}=\frac{-3+\sqrt{105}}{-24}
$