4/3y+1=2y

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

4/3y+1=2y

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6y^2+3y+4=0

a = -6; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-6)·4
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*-6}=\frac{-3-\sqrt{105}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-6}=\frac{-3+\sqrt{105}}{-12}
$