125/6x+181/2=31/3x+28

Solution for 125/6x+181/2=31/3x+28 equation:

125/6x+181/2=31/3x+28

We move all terms to the left:

125/6x+181/2-(31/3x+28)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+28)!=0

x∈R


We get rid of parentheses

125/6x-31/3x-28+181/2=0

We calculate fractions


9774x^2/72x^2+1500x/72x^2+(-744x)/72x^2-28=0

We multiply all the terms by the denominator


9774x^2+1500x+(-744x)-28*72x^2=0

Wy multiply elements

9774x^2-2016x^2+1500x+(-744x)=0

We get rid of parentheses

9774x^2-2016x^2+1500x-744x=0

We add all the numbers together, and all the variables

7758x^2+756x=0

a = 7758; b = 756; c = 0;
Δ = b2-4ac
Δ = 7562-4·7758·0
Δ = 571536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{571536}=756$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(756)-756}{2*7758}=\frac{-1512}{15516}
=-42/431
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(756)+756}{2*7758}=\frac{0}{15516}
=0
$