4x-1/6x+2=0

Solution for 4x-1/6x+2=0 equation:

4x-1/6x+2=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


4x*6x+2*6x-1=0

Wy multiply elements

24x^2+12x-1=0

a = 24; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·24·(-1)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*24}=\frac{-12-4\sqrt{15}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*24}=\frac{-12+4\sqrt{15}}{48}
$