1/2x-1/6x+3/2=-8

Solution for 1/2x-1/6x+3/2=-8 equation:

1/2x-1/6x+3/2=-8

We move all terms to the left:

1/2x-1/6x+3/2-(-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-1/6x+8+3/2=0

We calculate fractions


6x/48x^2+(-8x)/48x^2+18x/48x^2+8=0

We multiply all the terms by the denominator


6x+(-8x)+18x+8*48x^2=0

We add all the numbers together, and all the variables

24x+(-8x)+8*48x^2=0

Wy multiply elements

384x^2+24x+(-8x)=0

We get rid of parentheses

384x^2+24x-8x=0

We add all the numbers together, and all the variables

384x^2+16x=0

a = 384; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·384·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*384}=\frac{-32}{768}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*384}=\frac{0}{768}
=0
$