3x=4-8/16x

Solution for 3x=4-8/16x equation:

3x=4-8/16x

We move all terms to the left:

3x-(4-8/16x)=0


Domain of the equation: 16x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-8/16x+4)=0

We get rid of parentheses

3x+8/16x-4=0

We multiply all the terms by the denominator


3x*16x-4*16x+8=0

Wy multiply elements

48x^2-64x+8=0

a = 48; b = -64; c = +8;
Δ = b2-4ac
Δ = -642-4·48·8
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{10}}{2*48}=\frac{64-16\sqrt{10}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{10}}{2*48}=\frac{64+16\sqrt{10}}{96}
$