2x+1/2x=35

Solution for 2x+1/2x=35 equation:

2x+1/2x=35

We move all terms to the left:

2x+1/2x-(35)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-35*2x+1=0

Wy multiply elements

4x^2-70x+1=0

a = 4; b = -70; c = +1;
Δ = b2-4ac
Δ = -702-4·4·1
Δ = 4884
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:

$\sqrt{\Delta}=\sqrt{4884}=\sqrt{4*1221}=\sqrt{4}*\sqrt{1221}=2\sqrt{1221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1221}}{2*4}=\frac{70-2\sqrt{1221}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1221}}{2*4}=\frac{70+2\sqrt{1221}}{8}
$