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

Solution for X+1/x+2-x+3/6x=0 equation:

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


Domain of the equation: X!=0

X∈R



Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We add all the numbers together, and all the variables

1/X+3/6X+2=0

We calculate fractions


6X/6X^2+3X/6X^2+2=0

We multiply all the terms by the denominator


6X+3X+2*6X^2=0

We add all the numbers together, and all the variables

9X+2*6X^2=0

Wy multiply elements

12X^2+9X=0

a = 12; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·12·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*12}=\frac{-18}{24}
=-3/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*12}=\frac{0}{24}
=0
$