x+2x+3x+4x/x(x)=9

Solution for x+2x+3x+4x/x(x)=9 equation:

x+2x+3x+4x/x(x)=9

We move all terms to the left:

x+2x+3x+4x/x(x)-(9)=0


Domain of the equation: xx!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x+4x/xx-9=0

We multiply all the terms by the denominator


6x*xx+4x-9*xx=0

We add all the numbers together, and all the variables

4x+6x*xx-9*xx=0

Wy multiply elements

6x^2+4x-9x=0

We add all the numbers together, and all the variables

6x^2-5x=0

a = 6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·6·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*6}=\frac{10}{12}
=5/6
$