6/x-12=19/2x-3

Solution for 6/x-12=19/2x-3 equation:

6/x-12=19/2x-3

We move all terms to the left:

6/x-12-(19/2x-3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

6/x-19/2x+3-12=0

We calculate fractions


12x/2x^2+(-19x)/2x^2+3-12=0

We add all the numbers together, and all the variables

12x/2x^2+(-19x)/2x^2-9=0

We multiply all the terms by the denominator


12x+(-19x)-9*2x^2=0

Wy multiply elements

-18x^2+12x+(-19x)=0

We get rid of parentheses

-18x^2+12x-19x=0

We add all the numbers together, and all the variables

-18x^2-7x=0

a = -18; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-18)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-18}=\frac{14}{-36}
=-7/18
$