6/7s-10=2/s-6

Solution for 6/7s-10=2/s-6 equation:

6/7s-10=2/s-6

We move all terms to the left:

6/7s-10-(2/s-6)=0


Domain of the equation: 7s!=0

s!=0/7

s!=0

s∈R



Domain of the equation: s-6)!=0

s∈R


We get rid of parentheses

6/7s-2/s+6-10=0

We calculate fractions


6s/7s^2+(-14s)/7s^2+6-10=0

We add all the numbers together, and all the variables

6s/7s^2+(-14s)/7s^2-4=0

We multiply all the terms by the denominator


6s+(-14s)-4*7s^2=0

Wy multiply elements

-28s^2+6s+(-14s)=0

We get rid of parentheses

-28s^2+6s-14s=0

We add all the numbers together, and all the variables

-28s^2-8s=0

a = -28; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-28)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-28}=\frac{0}{-56}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-28}=\frac{16}{-56}
=-2/7
$