2x+1/2x=100

Solution for 2x+1/2x=100 equation:

2x+1/2x=100

We move all terms to the left:

2x+1/2x-(100)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-100*2x+1=0

Wy multiply elements

4x^2-200x+1=0

a = 4; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·4·1
Δ = 39984
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:

$\sqrt{\Delta}=\sqrt{39984}=\sqrt{784*51}=\sqrt{784}*\sqrt{51}=28\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-28\sqrt{51}}{2*4}=\frac{200-28\sqrt{51}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+28\sqrt{51}}{2*4}=\frac{200+28\sqrt{51}}{8}
$