3(1/2x-6)=-4-1/4x

Solution for 3(1/2x-6)=-4-1/4x equation:

3(1/2x-6)=-4-1/4x

We move all terms to the left:

3(1/2x-6)-(-4-1/4x)=0


Domain of the equation: 2x-6)!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(1/2x-6)-(-1/4x-4)=0

We multiply parentheses

3x-(-1/4x-4)-18=0

We get rid of parentheses

3x+1/4x+4-18=0

We multiply all the terms by the denominator


3x*4x+4*4x-18*4x+1=0

Wy multiply elements

12x^2+16x-72x+1=0

We add all the numbers together, and all the variables

12x^2-56x+1=0

a = 12; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·12·1
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{193}}{2*12}=\frac{56-4\sqrt{193}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{193}}{2*12}=\frac{56+4\sqrt{193}}{24}
$