54-5/8x=48-1/4x

Solution for 54-5/8x=48-1/4x equation:

54-5/8x=48-1/4x

We move all terms to the left:

54-5/8x-(48-1/4x)=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+48)+54=0

We get rid of parentheses

-5/8x+1/4x-48+54=0

We calculate fractions


(-20x)/32x^2+8x/32x^2-48+54=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

192x^2+8x-20x=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{0}{384}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*192}=\frac{24}{384}
=1/16
$