6x-1/x+3=2x+1

Solution for 6x-1/x+3=2x+1 equation:

6x-1/x+3=2x+1

We move all terms to the left:

6x-1/x+3-(2x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6x-1/x-2x-1+3=0

We multiply all the terms by the denominator


6x*x-2x*x-1*x+3*x-1=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2+2x-1=0

a = 4; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·4·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*4}=\frac{-2-2\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*4}=\frac{-2+2\sqrt{5}}{8}
$