5/3x-7/12x=13/6

Solution for 5/3x-7/12x=13/6 equation:

5/3x-7/12x=13/6

We move all terms to the left:

5/3x-7/12x-(13/6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-7/12x-(+13/6)=0

We get rid of parentheses

5/3x-7/12x-13/6=0

We calculate fractions


(-468x^2)/1296x^2+2160x/1296x^2+(-756x)/1296x^2=0

We multiply all the terms by the denominator


(-468x^2)+2160x+(-756x)=0

We get rid of parentheses

-468x^2+2160x-756x=0

We add all the numbers together, and all the variables

-468x^2+1404x=0

a = -468; b = 1404; c = 0;
Δ = b2-4ac
Δ = 14042-4·(-468)·0
Δ = 1971216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1971216}=1404$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1404)-1404}{2*-468}=\frac{-2808}{-936}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1404)+1404}{2*-468}=\frac{0}{-936}
=0
$