3x+2x/x=120

Solution for 3x+2x/x=120 equation:

3x+2x/x=120

We move all terms to the left:

3x+2x/x-(120)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x+2x-120*x=0

We add all the numbers together, and all the variables

-118x+3x*x=0

Wy multiply elements

3x^2-118x=0

a = 3; b = -118; c = 0;
Δ = b2-4ac
Δ = -1182-4·3·0
Δ = 13924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13924}=118$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-118}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+118}{2*3}=\frac{236}{6}
=39+1/3
$