(1/4x+12)=1/2x

Solution for (1/4x+12)=1/2x equation:

(1/4x+12)=1/2x

We move all terms to the left:

(1/4x+12)-(1/2x)=0


Domain of the equation: 4x+12)!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(1/4x+12)-(+1/2x)=0

We get rid of parentheses

1/4x-1/2x+12=0

We calculate fractions


2x/8x^2+(-4x)/8x^2+12=0

We multiply all the terms by the denominator


2x+(-4x)+12*8x^2=0

Wy multiply elements

96x^2+2x+(-4x)=0

We get rid of parentheses

96x^2+2x-4x=0

We add all the numbers together, and all the variables

96x^2-2x=0

a = 96; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·96·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*96}=\frac{0}{192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*96}=\frac{4}{192}
=1/48
$