9/x=-3/3x-7

Solution for 9/x=-3/3x-7 equation:

9/x=-3/3x-7

We move all terms to the left:

9/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

9/x+3/3x+7=0

We calculate fractions


27x/3x^2+3x/3x^2+7=0

We multiply all the terms by the denominator


27x+3x+7*3x^2=0

We add all the numbers together, and all the variables

30x+7*3x^2=0

Wy multiply elements

21x^2+30x=0

a = 21; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·21·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*21}=\frac{-60}{42}
=-1+3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*21}=\frac{0}{42}
=0
$