12-2x=1/4x

Solution for 12-2x=1/4x equation:

12-2x=1/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+48x-1=0

a = -8; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·(-8)·(-1)
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{142}}{2*-8}=\frac{-48-4\sqrt{142}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{142}}{2*-8}=\frac{-48+4\sqrt{142}}{-16}
$