2/x+2+8/3x+6=-9

Solution for 2/x+2+8/3x+6=-9 equation:

2/x+2+8/3x+6=-9

We move all terms to the left:

2/x+2+8/3x+6-(-9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+8/3x+17=0

We calculate fractions


6x/3x^2+8x/3x^2+17=0

We multiply all the terms by the denominator


6x+8x+17*3x^2=0

We add all the numbers together, and all the variables

14x+17*3x^2=0

Wy multiply elements

51x^2+14x=0

a = 51; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·51·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*51}=\frac{-28}{102}
=-14/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*51}=\frac{0}{102}
=0
$