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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-4)!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

4x-1/2x+4-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2+8x-8x-1=0

We add all the numbers together, and all the variables

8x^2-1=0

a = 8; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*8}=\frac{0-4\sqrt{2}}{16}
=-\frac{4\sqrt{2}}{16}
=-\frac{\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*8}=\frac{0+4\sqrt{2}}{16}
=\frac{4\sqrt{2}}{16}
=\frac{\sqrt{2}}{4}
$