X+2x+1/32x=120

Solution for X+2x+1/32x=120 equation:

X+2X+1/32X=120

We move all terms to the left:

X+2X+1/32X-(120)=0


Domain of the equation: 32X!=0

X!=0/32

X!=0

X∈R


We add all the numbers together, and all the variables

3X+1/32X-120=0

We multiply all the terms by the denominator


3X*32X-120*32X+1=0

Wy multiply elements

96X^2-3840X+1=0

a = 96; b = -3840; c = +1;
Δ = b2-4ac
Δ = -38402-4·96·1
Δ = 14745216
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:

$\sqrt{\Delta}=\sqrt{14745216}=\sqrt{64*230394}=\sqrt{64}*\sqrt{230394}=8\sqrt{230394}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3840)-8\sqrt{230394}}{2*96}=\frac{3840-8\sqrt{230394}}{192}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3840)+8\sqrt{230394}}{2*96}=\frac{3840+8\sqrt{230394}}{192}
$