-6/x=-7/3x+4

Solution for -6/x=-7/3x+4 equation:

-6/x=-7/3x+4

We move all terms to the left:

-6/x-(-7/3x+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

-6/x+7/3x-4=0

We calculate fractions


(-18x)/3x^2+7x/3x^2-4=0

We multiply all the terms by the denominator


(-18x)+7x-4*3x^2=0

We add all the numbers together, and all the variables

7x+(-18x)-4*3x^2=0

Wy multiply elements

-12x^2+7x+(-18x)=0

We get rid of parentheses

-12x^2+7x-18x=0

We add all the numbers together, and all the variables

-12x^2-11x=0

a = -12; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-12)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-12}=\frac{22}{-24}
=-11/12
$