1/3x-19/6=7/2x

Solution for 1/3x-19/6=7/2x equation:

1/3x-19/6=7/2x

We move all terms to the left:

1/3x-19/6-(7/2x)=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-(+7/2x)-19/6=0

We get rid of parentheses

1/3x-7/2x-19/6=0

We calculate fractions


(-228x^2)/216x^2+72x/216x^2+(-756x)/216x^2=0

We multiply all the terms by the denominator


(-228x^2)+72x+(-756x)=0

We get rid of parentheses

-228x^2+72x-756x=0

We add all the numbers together, and all the variables

-228x^2-684x=0

a = -228; b = -684; c = 0;
Δ = b2-4ac
Δ = -6842-4·(-228)·0
Δ = 467856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{467856}=684$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-684)-684}{2*-228}=\frac{0}{-456}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-684)+684}{2*-228}=\frac{1368}{-456}
=-3
$