5/12x-2/7x=20

Solution for 5/12x-2/7x=20 equation:

5/12x-2/7x=20

We move all terms to the left:

5/12x-2/7x-(20)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


35x/84x^2+(-24x)/84x^2-20=0

We multiply all the terms by the denominator


35x+(-24x)-20*84x^2=0

Wy multiply elements

-1680x^2+35x+(-24x)=0

We get rid of parentheses

-1680x^2+35x-24x=0

We add all the numbers together, and all the variables

-1680x^2+11x=0

a = -1680; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-1680)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-1680}=\frac{-22}{-3360}
=11/1680
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-1680}=\frac{0}{-3360}
=0
$