-1x=1/3x-2

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

-1x=1/3x-2

We move all terms to the left:

-1x-(1/3x-2)=0


Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

-1x-1/3x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -3; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-3)·(-1)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*-3}=\frac{-6-2\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*-3}=\frac{-6+2\sqrt{6}}{-6}
$