3x+1/4x-2=0

Solution for 3x+1/4x-2=0 equation:

3x+1/4x-2=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-8x+1=0

a = 12; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·12·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*12}=\frac{4}{24}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*12}=\frac{12}{24}
=1/2
$