2x+1/4x=3

Solution for 2x+1/4x=3 equation:

2x+1/4x=3

We move all terms to the left:

2x+1/4x-(3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-3*4x+1=0

Wy multiply elements

8x^2-12x+1=0

a = 8; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·8·1
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{7}}{2*8}=\frac{12-4\sqrt{7}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{7}}{2*8}=\frac{12+4\sqrt{7}}{16}
$