6/4x+x=12

Solution for 6/4x+x=12 equation:

6/4x+x=12

We move all terms to the left:

6/4x+x-(12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+6/4x-12=0

We multiply all the terms by the denominator


x*4x-12*4x+6=0

Wy multiply elements

4x^2-48x+6=0

a = 4; b = -48; c = +6;
Δ = b2-4ac
Δ = -482-4·4·6
Δ = 2208
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:

$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{138}}{2*4}=\frac{48-4\sqrt{138}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{138}}{2*4}=\frac{48+4\sqrt{138}}{8}
$