-1/3x+5=x-1

Solution for -1/3x+5=x-1 equation:

-1/3x+5=x-1

We move all terms to the left:

-1/3x+5-(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+5=0

We multiply all the terms by the denominator


-x*3x+1*3x+5*3x-1=0

Wy multiply elements

-3x^2+3x+15x-1=0

We add all the numbers together, and all the variables

-3x^2+18x-1=0

a = -3; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-3)·(-1)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{78}}{2*-3}=\frac{-18-2\sqrt{78}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{78}}{2*-3}=\frac{-18+2\sqrt{78}}{-6}
$