x+1/2x=8

Solution for x+1/2x=8 equation:

x+1/2x=8

We move all terms to the left:

x+1/2x-(8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-8*2x+1=0

Wy multiply elements

2x^2-16x+1=0

a = 2; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·2·1
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{62}}{2*2}=\frac{16-2\sqrt{62}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{62}}{2*2}=\frac{16+2\sqrt{62}}{4}
$