1/6x+4x=4

Solution for 1/6x+4x=4 equation:

1/6x+4x=4

We move all terms to the left:

1/6x+4x-(4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/6x-4=0

We multiply all the terms by the denominator


4x*6x-4*6x+1=0

Wy multiply elements

24x^2-24x+1=0

a = 24; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·24·1
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{30}}{2*24}=\frac{24-4\sqrt{30}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{30}}{2*24}=\frac{24+4\sqrt{30}}{48}
$