2x+1/2x=117

Solution for 2x+1/2x=117 equation:

2x+1/2x=117

We move all terms to the left:

2x+1/2x-(117)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-117*2x+1=0

Wy multiply elements

4x^2-234x+1=0

a = 4; b = -234; c = +1;
Δ = b2-4ac
Δ = -2342-4·4·1
Δ = 54740
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:

$\sqrt{\Delta}=\sqrt{54740}=\sqrt{4*13685}=\sqrt{4}*\sqrt{13685}=2\sqrt{13685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-2\sqrt{13685}}{2*4}=\frac{234-2\sqrt{13685}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+2\sqrt{13685}}{2*4}=\frac{234+2\sqrt{13685}}{8}
$