1/4x-5/8x=30-54

Solution for 1/4x-5/8x=30-54 equation:

1/4x-5/8x=30-54

We move all terms to the left:

1/4x-5/8x-(30-54)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-5/8x-(-24)=0

We add all the numbers together, and all the variables

1/4x-5/8x+24=0

We calculate fractions


8x/32x^2+(-20x)/32x^2+24=0

We multiply all the terms by the denominator


8x+(-20x)+24*32x^2=0

Wy multiply elements

768x^2+8x+(-20x)=0

We get rid of parentheses

768x^2+8x-20x=0

We add all the numbers together, and all the variables

768x^2-12x=0

a = 768; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·768·0
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*768}=\frac{0}{1536}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*768}=\frac{24}{1536}
=1/64
$