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

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

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

We move all terms to the left:

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


Domain of the equation: 42x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(x-1)-(+1/42x)=0

We multiply parentheses

4x-(+1/42x)-4=0

We get rid of parentheses

4x-1/42x-4=0

We multiply all the terms by the denominator


4x*42x-4*42x-1=0

Wy multiply elements

168x^2-168x-1=0

a = 168; b = -168; c = -1;
Δ = b2-4ac
Δ = -1682-4·168·(-1)
Δ = 28896
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:

$\sqrt{\Delta}=\sqrt{28896}=\sqrt{16*1806}=\sqrt{16}*\sqrt{1806}=4\sqrt{1806}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-4\sqrt{1806}}{2*168}=\frac{168-4\sqrt{1806}}{336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+4\sqrt{1806}}{2*168}=\frac{168+4\sqrt{1806}}{336}
$