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

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

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

We move all terms to the left:

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


Domain of the equation: 2x*1!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x-8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x/8x^2+(-6x)/8x^2+8=0

We multiply all the terms by the denominator


2x+(-6x)+8*8x^2=0

Wy multiply elements

64x^2+2x+(-6x)=0

We get rid of parentheses

64x^2+2x-6x=0

We add all the numbers together, and all the variables

64x^2-4x=0

a = 64; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·64·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*64}=\frac{8}{128}
=1/16
$