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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


256x^2/512x^2+128x/512x^2+(-192x)/512x^2+(-128x)/512x^2=0

We multiply all the terms by the denominator


256x^2+128x+(-192x)+(-128x)=0

We get rid of parentheses

256x^2+128x-192x-128x=0

We add all the numbers together, and all the variables

256x^2-192x=0

a = 256; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·256·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*256}=\frac{0}{512}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*256}=\frac{384}{512}
=3/4
$