1/8-3/4x=1/2x

Solution for 1/8-3/4x=1/2x equation:

1/8-3/4x=1/2x

We move all terms to the left:

1/8-3/4x-(1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(+1/2x)+1/8=0

We get rid of parentheses

-3/4x-1/2x+1/8=0

We calculate fractions


16x^2/512x^2+(-384x)/512x^2+(-256x)/512x^2=0

We multiply all the terms by the denominator


16x^2+(-384x)+(-256x)=0

We get rid of parentheses

16x^2-384x-256x=0

We add all the numbers together, and all the variables

16x^2-640x=0

a = 16; b = -640; c = 0;
Δ = b2-4ac
Δ = -6402-4·16·0
Δ = 409600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{409600}=640$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-640)-640}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-640)+640}{2*16}=\frac{1280}{32}
=40
$