8x-(3/2x)=1

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

8x-(3/2x)=1

We move all terms to the left:

8x-(3/2x)-(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

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

We get rid of parentheses

8x-3/2x-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2-2x-3=0

a = 16; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·16·(-3)
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*16}=\frac{-12}{32}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*16}=\frac{16}{32}
=1/2
$