-8/x=9/3x-7

Solution for -8/x=9/3x-7 equation:

-8/x=9/3x-7

We move all terms to the left:

-8/x-(9/3x-7)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

-8/x-9/3x+7=0

We calculate fractions


(-24x)/3x^2+(-9x)/3x^2+7=0

We multiply all the terms by the denominator


(-24x)+(-9x)+7*3x^2=0

Wy multiply elements

21x^2+(-24x)+(-9x)=0

We get rid of parentheses

21x^2-24x-9x=0

We add all the numbers together, and all the variables

21x^2-33x=0

a = 21; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·21·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*21}=\frac{0}{42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*21}=\frac{66}{42}
=1+4/7
$