6x+2=3/x

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

6x+2=3/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6x-3/x+2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x+6x*x-3=0

Wy multiply elements

6x^2+2x-3=0

a = 6; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·6·(-3)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*6}=\frac{-2-2\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*6}=\frac{-2+2\sqrt{19}}{12}
$