1/2x+3=1/8x-12

Solution for 1/2x+3=1/8x-12 equation:

1/2x+3=1/8x-12

We move all terms to the left:

1/2x+3-(1/8x-12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x-12)!=0

x∈R


We get rid of parentheses

1/2x-1/8x+12+3=0

We calculate fractions


8x/16x^2+(-2x)/16x^2+12+3=0

We add all the numbers together, and all the variables

8x/16x^2+(-2x)/16x^2+15=0

We multiply all the terms by the denominator


8x+(-2x)+15*16x^2=0

Wy multiply elements

240x^2+8x+(-2x)=0

We get rid of parentheses

240x^2+8x-2x=0

We add all the numbers together, and all the variables

240x^2+6x=0

a = 240; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·240·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*240}=\frac{-12}{480}
=-1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*240}=\frac{0}{480}
=0
$