4/3y-y=6

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

4/3y-y=6

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+4/3y-6=0

We multiply all the terms by the denominator


-1y*3y-6*3y+4=0

Wy multiply elements

-3y^2-18y+4=0

a = -3; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·(-3)·4
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*-3}=\frac{18-2\sqrt{93}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*-3}=\frac{18+2\sqrt{93}}{-6}
$