12/s=6.s

Solution for 12/s=6.s equation:

12/s=6.s

We move all terms to the left:

12/s-(6.s)=0


Domain of the equation: s!=0

s∈R


We add all the numbers together, and all the variables

12/s-(+6.s)=0

We get rid of parentheses

12/s-6.s=0

We multiply all the terms by the denominator


-(6.s)*s+12=0

We add all the numbers together, and all the variables

-(+6.s)*s+12=0

We multiply parentheses

-6s^2+12=0

a = -6; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-6)·12
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-6}=\frac{0-12\sqrt{2}}{-12}
=-\frac{12\sqrt{2}}{-12}
=-\frac{\sqrt{2}}{-1}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-6}=\frac{0+12\sqrt{2}}{-12}
=\frac{12\sqrt{2}}{-12}
=\frac{\sqrt{2}}{-1}
$