x/2x+4+3x=39

Solution for x/2x+4+3x=39 equation:

x/2x+4+3x=39

We move all terms to the left:

x/2x+4+3x-(39)=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-35=0

We multiply all the terms by the denominator


3x*2x+x-35*2x=0

We add all the numbers together, and all the variables

x+3x*2x-35*2x=0

Wy multiply elements

6x^2+x-70x=0

We add all the numbers together, and all the variables

6x^2-69x=0

a = 6; b = -69; c = 0;
Δ = b2-4ac
Δ = -692-4·6·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-69}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+69}{2*6}=\frac{138}{12}
=11+1/2
$