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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

2x-(-4(-1x+1/4))-12=0

We multiply all the terms by the denominator


2x*4))-(-4(-1x+1-12*4))=0

We add all the numbers together, and all the variables

2x*4))-(-4(-1x-47))=0

We add all the numbers together, and all the variables

-1x+2x*4))-(-4(=0

Wy multiply elements

8x^2-1x=0

a = 8; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·8·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*8}=\frac{2}{16}
=1/8
$