16/4x-8=25/3x

Solution for 16/4x-8=25/3x equation:

16/4x-8=25/3x

We move all terms to the left:

16/4x-8-(25/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

16/4x-(+25/3x)-8=0

We get rid of parentheses

16/4x-25/3x-8=0

We calculate fractions


48x/12x^2+(-100x)/12x^2-8=0

We multiply all the terms by the denominator


48x+(-100x)-8*12x^2=0

Wy multiply elements

-96x^2+48x+(-100x)=0

We get rid of parentheses

-96x^2+48x-100x=0

We add all the numbers together, and all the variables

-96x^2-52x=0

a = -96; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·(-96)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*-96}=\frac{104}{-192}
=-13/24
$