5/8+1/4x=1/2x

Solution for 5/8+1/4x=1/2x equation:

5/8+1/4x=1/2x

We move all terms to the left:

5/8+1/4x-(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

1/4x-(+1/2x)+5/8=0

We get rid of parentheses

1/4x-1/2x+5/8=0

We calculate fractions


80x^2/512x^2+128x/512x^2+(-256x)/512x^2=0

We multiply all the terms by the denominator


80x^2+128x+(-256x)=0

We get rid of parentheses

80x^2+128x-256x=0

We add all the numbers together, and all the variables

80x^2-128x=0

a = 80; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·80·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*80}=\frac{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*80}=\frac{256}{160}
=1+3/5
$