2x+28=4/8x

Solution for 2x+28=4/8x equation:

2x+28=4/8x

We move all terms to the left:

2x+28-(4/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+4/8x)+28=0

We get rid of parentheses

2x-4/8x+28=0

We multiply all the terms by the denominator


2x*8x+28*8x-4=0

Wy multiply elements

16x^2+224x-4=0

a = 16; b = 224; c = -4;
Δ = b2-4ac
Δ = 2242-4·16·(-4)
Δ = 50432
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:

$\sqrt{\Delta}=\sqrt{50432}=\sqrt{256*197}=\sqrt{256}*\sqrt{197}=16\sqrt{197}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-16\sqrt{197}}{2*16}=\frac{-224-16\sqrt{197}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+16\sqrt{197}}{2*16}=\frac{-224+16\sqrt{197}}{32}
$