-9/x=3/3x+8

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

-9/x=3/3x+8

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-27x)/3x^2+(-3x)/3x^2-8=0

We multiply all the terms by the denominator


(-27x)+(-3x)-8*3x^2=0

Wy multiply elements

-24x^2+(-27x)+(-3x)=0

We get rid of parentheses

-24x^2-27x-3x=0

We add all the numbers together, and all the variables

-24x^2-30x=0

a = -24; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-24)·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*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-24}=\frac{60}{-48}
=-1+1/4
$