8=4x+1/2x

Solution for 8=4x+1/2x equation:

8=4x+1/2x

We move all terms to the left:

8-(4x+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+4x+1/2x)+8=0

We get rid of parentheses

-4x-1/2x+8=0

We multiply all the terms by the denominator


-4x*2x+8*2x-1=0

Wy multiply elements

-8x^2+16x-1=0

a = -8; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·(-8)·(-1)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{14}}{2*-8}=\frac{-16-4\sqrt{14}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{14}}{2*-8}=\frac{-16+4\sqrt{14}}{-16}
$