1/2x+4=4+4x

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

1/2x+4=4+4x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2x-4x-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}
$