4/3y+6=4y

Solution for 4/3y+6=4y equation:

4/3y+6=4y

We move all terms to the left:

4/3y+6-(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+4/3y+6=0

We multiply all the terms by the denominator


-4y*3y+6*3y+4=0

Wy multiply elements

-12y^2+18y+4=0

a = -12; b = 18; c = +4;
Δ = b2-4ac
Δ = 182-4·(-12)·4
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{129}}{2*-12}=\frac{-18-2\sqrt{129}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{129}}{2*-12}=\frac{-18+2\sqrt{129}}{-24}
$