6x-2/x=1

Solution for 6x-2/x=1 equation:

6x-2/x=1

We move all terms to the left:

6x-2/x-(1)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x-1*x-2=0

We add all the numbers together, and all the variables

-1x+6x*x-2=0

Wy multiply elements

6x^2-1x-2=0

a = 6; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·6·(-2)
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*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*6}=\frac{8}{12}
=2/3
$