4x+12x+1/2x=161/2x

Solution for 4x+12x+1/2x=161/2x equation:

4x+12x+1/2x=161/2x

We move all terms to the left:

4x+12x+1/2x-(161/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x+12x+1/2x-(+161/2x)=0

We add all the numbers together, and all the variables

16x+1/2x-(+161/2x)=0

We get rid of parentheses

16x+1/2x-161/2x=0

We multiply all the terms by the denominator


16x*2x+1-161=0

We add all the numbers together, and all the variables

16x*2x-160=0

Wy multiply elements

32x^2-160=0

a = 32; b = 0; c = -160;
Δ = b2-4ac
Δ = 02-4·32·(-160)
Δ = 20480
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:

$\sqrt{\Delta}=\sqrt{20480}=\sqrt{4096*5}=\sqrt{4096}*\sqrt{5}=64\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{5}}{2*32}=\frac{0-64\sqrt{5}}{64}
=-\frac{64\sqrt{5}}{64}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{5}}{2*32}=\frac{0+64\sqrt{5}}{64}
=\frac{64\sqrt{5}}{64}
=\sqrt{5}
$