6/7s-5/6s=1/21

Solution for 6/7s-5/6s=1/21 equation:

6/7s-5/6s=1/21

We move all terms to the left:

6/7s-5/6s-(1/21)=0


Domain of the equation: 7s!=0

s!=0/7

s!=0

s∈R



Domain of the equation: 6s!=0

s!=0/6

s!=0

s∈R


We add all the numbers together, and all the variables

6/7s-5/6s-(+1/21)=0

We get rid of parentheses

6/7s-5/6s-1/21=0

We calculate fractions


(-252s^2)/1764s^2+1512s/1764s^2+(-1470s)/1764s^2=0

We multiply all the terms by the denominator


(-252s^2)+1512s+(-1470s)=0

We get rid of parentheses

-252s^2+1512s-1470s=0

We add all the numbers together, and all the variables

-252s^2+42s=0

a = -252; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-252)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-252}=\frac{-84}{-504}
=1/6
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-252}=\frac{0}{-504}
=0
$