4x+1/2x-4=-1/2x+16

Solution for 4x+1/2x-4=-1/2x+16 equation:

4x+1/2x-4=-1/2x+16

We move all terms to the left:

4x+1/2x-4-(-1/2x+16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

4x+1/2x+1/2x-16-4=0

We multiply all the terms by the denominator


4x*2x-16*2x-4*2x+1+1=0

We add all the numbers together, and all the variables

4x*2x-16*2x-4*2x+2=0

Wy multiply elements

8x^2-32x-8x+2=0

We add all the numbers together, and all the variables

8x^2-40x+2=0

a = 8; b = -40; c = +2;
Δ = b2-4ac
Δ = -402-4·8·2
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16\sqrt{6}}{2*8}=\frac{40-16\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16\sqrt{6}}{2*8}=\frac{40+16\sqrt{6}}{16}
$