6/x=2x-1

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

6/x=2x-1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6/x-2x+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x-2x*x+6=0

Wy multiply elements

-2x^2+x+6=0

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