-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 = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{141}}{2*-12}=\frac{-48-4\sqrt{141}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{141}}{2*-12}=\frac{-48+4\sqrt{141}}{-24}
$