1/3y-y=-2

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

1/3y-y=-2

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3y^2+6y+1=0

a = -3; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-3)·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*-3}=\frac{-6-4\sqrt{3}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*-3}=\frac{-6+4\sqrt{3}}{-6}
$