(1/2x)+(1/4x)=4

Solution for (1/2x)+(1/4x)=4 equation:

(1/2x)+(1/4x)=4

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-4*8x^2=0

Wy multiply elements

-32x^2+6x=0

a = -32; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-32)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-32}=\frac{-12}{-64}
=3/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-32}=\frac{0}{-64}
=0
$