1/2x=1/8x+120

Solution for 1/2x=1/8x+120 equation:

1/2x=1/8x+120

We move all terms to the left:

1/2x-(1/8x+120)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+120)!=0

x∈R


We get rid of parentheses

1/2x-1/8x-120=0

We calculate fractions


8x/16x^2+(-2x)/16x^2-120=0

We multiply all the terms by the denominator


8x+(-2x)-120*16x^2=0

Wy multiply elements

-1920x^2+8x+(-2x)=0

We get rid of parentheses

-1920x^2+8x-2x=0

We add all the numbers together, and all the variables

-1920x^2+6x=0

a = -1920; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1920)·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*-1920}=\frac{-12}{-3840}
=1/320
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1920}=\frac{0}{-3840}
=0
$