12/x=x-1

Solution for 12/x=x-1 equation:

12/x=x-1

We move all terms to the left:

12/x-(x-1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

12/x-x+1=0

We multiply all the terms by the denominator


-x*x+1*x+12=0

We add all the numbers together, and all the variables

x-x*x+12=0

Wy multiply elements

-1x^2+x+12=0

a = -1; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-1)·12
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-1}=\frac{6}{-2}
=-3
$