x+4x=1/4x+12

Solution for x+4x=1/4x+12 equation:

x+4x=1/4x+12

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

5x-(1/4x+12)=0

We get rid of parentheses

5x-1/4x-12=0

We multiply all the terms by the denominator


5x*4x-12*4x-1=0

Wy multiply elements

20x^2-48x-1=0

a = 20; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·20·(-1)
Δ = 2384
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:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{149}}{2*20}=\frac{48-4\sqrt{149}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{149}}{2*20}=\frac{48+4\sqrt{149}}{40}
$