3x-12=1/4x+6

Solution for 3x-12=1/4x+6 equation:

3x-12=1/4x+6

We move all terms to the left:

3x-12-(1/4x+6)=0


Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

3x-1/4x-6-12=0

We multiply all the terms by the denominator


3x*4x-6*4x-12*4x-1=0

Wy multiply elements

12x^2-24x-48x-1=0

We add all the numbers together, and all the variables

12x^2-72x-1=0

a = 12; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·12·(-1)
Δ = 5232
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:

$\sqrt{\Delta}=\sqrt{5232}=\sqrt{16*327}=\sqrt{16}*\sqrt{327}=4\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{327}}{2*12}=\frac{72-4\sqrt{327}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{327}}{2*12}=\frac{72+4\sqrt{327}}{24}
$