1/4x=3+6x

Solution for 1/4x=3+6x equation:

1/4x=3+6x

We move all terms to the left:

1/4x-(3+6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(6x+3)=0

We get rid of parentheses

1/4x-6x-3=0

We multiply all the terms by the denominator


-6x*4x-3*4x+1=0

Wy multiply elements

-24x^2-12x+1=0

a = -24; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-24)·1
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-24}=\frac{12-4\sqrt{15}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-24}=\frac{12+4\sqrt{15}}{-48}
$