1/4x=3x-1

Solution for 1/4x=3x-1 equation:

1/4x=3x-1

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-3x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+4x+1=0

a = -12; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-12)·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-12}=\frac{-12}{-24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-12}=\frac{4}{-24}
=-1/6
$