(3x-8/2x)=1

Solution for (3x-8/2x)=1 equation:

(3x-8/2x)=1

We move all terms to the left:

(3x-8/2x)-(1)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3x-8/2x)-1=0

We get rid of parentheses

3x-8/2x-1=0

We multiply all the terms by the denominator


3x*2x-1*2x-8=0

Wy multiply elements

6x^2-2x-8=0

a = 6; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·6·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*6}=\frac{16}{12}
=1+1/3
$