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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-384x^2)/256x^2+128x/256x^2+(-32x)/256x^2=0

We multiply all the terms by the denominator


(-384x^2)+128x+(-32x)=0

We get rid of parentheses

-384x^2+128x-32x=0

We add all the numbers together, and all the variables

-384x^2+96x=0

a = -384; b = 96; c = 0;
Δ = b2-4ac
Δ = 962-4·(-384)·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96}{2*-384}=\frac{-192}{-768}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96}{2*-384}=\frac{0}{-768}
=0
$