x/9+3x/x=0

Solution for x/9+3x/x=0 equation:

x/9+3x/x=0


Domain of the equation: x!=0

x∈R


We calculate fractions


x^2/9x+27x/9x=0

We multiply all the terms by the denominator


x^2+27x=0

a = 1; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·1·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*1}=\frac{-54}{2}
=-27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*1}=\frac{0}{2}
=0
$