1/4x=3x-12

Solution for 1/4x=3x-12 equation:

1/4x=3x-12

We move all terms to the left:

1/4x-(3x-12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-3x+12=0

We multiply all the terms by the denominator


-3x*4x+12*4x+1=0

Wy multiply elements

-12x^2+48x+1=0

a = -12; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-12)·1
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-28\sqrt{3}}{2*-12}=\frac{-48-28\sqrt{3}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+28\sqrt{3}}{2*-12}=\frac{-48+28\sqrt{3}}{-24}
$