1/2x*4=2x+16

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

1/2x*4=2x+16

We move all terms to the left:

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


Domain of the equation: 2x*4!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2*4-128x*4+1=0

Wy multiply elements

-64x^2-512x+1=0

a = -64; b = -512; c = +1;
Δ = b2-4ac
Δ = -5122-4·(-64)·1
Δ = 262400
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:

$\sqrt{\Delta}=\sqrt{262400}=\sqrt{6400*41}=\sqrt{6400}*\sqrt{41}=80\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-512)-80\sqrt{41}}{2*-64}=\frac{512-80\sqrt{41}}{-128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-512)+80\sqrt{41}}{2*-64}=\frac{512+80\sqrt{41}}{-128}
$