5/8x-6=1/4x

Solution for 5/8x-6=1/4x equation:

5/8x-6=1/4x

We move all terms to the left:

5/8x-6-(1/4x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-(+1/4x)-6=0

We get rid of parentheses

5/8x-1/4x-6=0

We calculate fractions


20x/32x^2+(-8x)/32x^2-6=0

We multiply all the terms by the denominator


20x+(-8x)-6*32x^2=0

Wy multiply elements

-192x^2+20x+(-8x)=0

We get rid of parentheses

-192x^2+20x-8x=0

We add all the numbers together, and all the variables

-192x^2+12x=0

a = -192; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-192)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-192}=\frac{-24}{-384}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-192}=\frac{0}{-384}
=0
$