3/4x-5/8=23/24x-5

Solution for 3/4x-5/8=23/24x-5 equation:

3/4x-5/8=23/24x-5

We move all terms to the left:

3/4x-5/8-(23/24x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 24x-5)!=0

x∈R


We get rid of parentheses

3/4x-23/24x+5-5/8=0

We calculate fractions


(-960x^2)/6144x^2+4608x/6144x^2+(-5888x)/6144x^2+5=0

We multiply all the terms by the denominator


(-960x^2)+4608x+(-5888x)+5*6144x^2=0

Wy multiply elements

(-960x^2)+30720x^2+4608x+(-5888x)=0

We get rid of parentheses

-960x^2+30720x^2+4608x-5888x=0

We add all the numbers together, and all the variables

29760x^2-1280x=0

a = 29760; b = -1280; c = 0;
Δ = b2-4ac
Δ = -12802-4·29760·0
Δ = 1638400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1638400}=1280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1280)-1280}{2*29760}=\frac{0}{59520}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1280)+1280}{2*29760}=\frac{2560}{59520}
=4/93
$