1/3x-1=x-4

Solution for 1/3x-1=x-4 equation:

1/3x-1=x-4

We move all terms to the left:

1/3x-1-(x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+4-1=0

We multiply all the terms by the denominator


-x*3x+4*3x-1*3x+1=0

Wy multiply elements

-3x^2+12x-3x+1=0

We add all the numbers together, and all the variables

-3x^2+9x+1=0

a = -3; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·(-3)·1
Δ = 93
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{-(9)-\sqrt{93}}{2*-3}=\frac{-9-\sqrt{93}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{93}}{2*-3}=\frac{-9+\sqrt{93}}{-6}
$