1/3x-13/6=5/2x

Solution for 1/3x-13/6=5/2x equation:

1/3x-13/6=5/2x

We move all terms to the left:

1/3x-13/6-(5/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(+5/2x)-13/6=0

We get rid of parentheses

1/3x-5/2x-13/6=0

We calculate fractions


(-156x^2)/216x^2+72x/216x^2+(-540x)/216x^2=0

We multiply all the terms by the denominator


(-156x^2)+72x+(-540x)=0

We get rid of parentheses

-156x^2+72x-540x=0

We add all the numbers together, and all the variables

-156x^2-468x=0

a = -156; b = -468; c = 0;
Δ = b2-4ac
Δ = -4682-4·(-156)·0
Δ = 219024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{219024}=468$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-468}{2*-156}=\frac{0}{-312}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+468}{2*-156}=\frac{936}{-312}
=-3
$