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

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

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

We move all terms to the left:

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


Domain of the equation: 22x-42)!=0

x∈R


We get rid of parentheses

42x-1/22x+42-42=0

We multiply all the terms by the denominator


42x*22x+42*22x-42*22x-1=0

Wy multiply elements

924x^2+924x-924x-1=0

We add all the numbers together, and all the variables

924x^2-1=0

a = 924; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·924·(-1)
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{231}}{2*924}=\frac{0-4\sqrt{231}}{1848}
=-\frac{4\sqrt{231}}{1848}
=-\frac{\sqrt{231}}{462}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{231}}{2*924}=\frac{0+4\sqrt{231}}{1848}
=\frac{4\sqrt{231}}{1848}
=\frac{\sqrt{231}}{462}
$