x/2x+3x+4=44

Solution for x/2x+3x+4=44 equation:

x/2x+3x+4=44

We move all terms to the left:

x/2x+3x+4-(44)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+x/2x-40=0

We multiply all the terms by the denominator


3x*2x+x-40*2x=0

We add all the numbers together, and all the variables

x+3x*2x-40*2x=0

Wy multiply elements

6x^2+x-80x=0

We add all the numbers together, and all the variables

6x^2-79x=0

a = 6; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·6·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*6}=\frac{158}{12}
=13+1/6
$