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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-128x^2)/256x^2+128x/256x^2+(-160x)/256x^2-2=0

We multiply all the terms by the denominator


(-128x^2)+128x+(-160x)-2*256x^2=0

Wy multiply elements

(-128x^2)-512x^2+128x+(-160x)=0

We get rid of parentheses

-128x^2-512x^2+128x-160x=0

We add all the numbers together, and all the variables

-640x^2-32x=0

a = -640; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-640)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-640}=\frac{0}{-1280}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-640}=\frac{64}{-1280}
=-1/20
$