12/x+8=14/3x-9

Solution for 12/x+8=14/3x-9 equation:

12/x+8=14/3x-9

We move all terms to the left:

12/x+8-(14/3x-9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-9)!=0

x∈R


We get rid of parentheses

12/x-14/3x+9+8=0

We calculate fractions


36x/3x^2+(-14x)/3x^2+9+8=0

We add all the numbers together, and all the variables

36x/3x^2+(-14x)/3x^2+17=0

We multiply all the terms by the denominator


36x+(-14x)+17*3x^2=0

Wy multiply elements

51x^2+36x+(-14x)=0

We get rid of parentheses

51x^2+36x-14x=0

We add all the numbers together, and all the variables

51x^2+22x=0

a = 51; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·51·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*51}=\frac{-44}{102}
=-22/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*51}=\frac{0}{102}
=0
$