5x+x/3,x=9

Solution for 5x+x/3,x=9 equation:

5x+x/3.x=9

We move all terms to the left:

5x+x/3.x-(9)=0


Domain of the equation: 3.x!=0

x!=0/3.

x!=0

x∈R


We multiply all the terms by the denominator


5x*3.x+x-9*3.x=0

We add all the numbers together, and all the variables

x+5x*3.x-9*3.x=0

Wy multiply elements

15x^2+x-27x=0

We add all the numbers together, and all the variables

15x^2-26x=0

a = 15; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·15·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*15}=\frac{52}{30}
=1+11/15
$