x+1=1/2(4x)

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

x+1=1/2(4x)

We move all terms to the left:

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


Domain of the equation: 24x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/24x)+1=0

We get rid of parentheses

x-1/24x+1=0

We multiply all the terms by the denominator


x*24x+1*24x-1=0

Wy multiply elements

24x^2+24x-1=0

a = 24; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·24·(-1)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{42}}{2*24}=\frac{-24-4\sqrt{42}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{42}}{2*24}=\frac{-24+4\sqrt{42}}{48}
$