1/3x=x-1

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

1/3x=x-1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -3; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-3)·1
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{21}}{2*-3}=\frac{-3-\sqrt{21}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*-3}=\frac{-3+\sqrt{21}}{-6}
$