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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-9x)/3x^2+6x/3x^2-7=0

We multiply all the terms by the denominator


(-9x)+6x-7*3x^2=0

We add all the numbers together, and all the variables

6x+(-9x)-7*3x^2=0

Wy multiply elements

-21x^2+6x+(-9x)=0

We get rid of parentheses

-21x^2+6x-9x=0

We add all the numbers together, and all the variables

-21x^2-3x=0

a = -21; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-21)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-21}=\frac{6}{-42}
=-1/7
$