x+3x+2/x=120

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

x+3x+2/x=120

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+2/x-120=0

We multiply all the terms by the denominator


4x*x-120*x+2=0

We add all the numbers together, and all the variables

-120x+4x*x+2=0

Wy multiply elements

4x^2-120x+2=0

a = 4; b = -120; c = +2;
Δ = b2-4ac
Δ = -1202-4·4·2
Δ = 14368
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14368}=\sqrt{16*898}=\sqrt{16}*\sqrt{898}=4\sqrt{898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{898}}{2*4}=\frac{120-4\sqrt{898}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{898}}{2*4}=\frac{120+4\sqrt{898}}{8}
$