-5/x=3/3x+7

Solution for -5/x=3/3x+7 equation:

-5/x=3/3x+7

We move all terms to the left:

-5/x-(3/3x+7)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

-5/x-3/3x-7=0

We calculate fractions


(-15x)/3x^2+(-3x)/3x^2-7=0

We multiply all the terms by the denominator


(-15x)+(-3x)-7*3x^2=0

Wy multiply elements

-21x^2+(-15x)+(-3x)=0

We get rid of parentheses

-21x^2-15x-3x=0

We add all the numbers together, and all the variables

-21x^2-18x=0

a = -21; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-21)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-21}=\frac{36}{-42}
=-6/7
$