10/11*s=6

Solution for 10/11*s=6 equation:

10/11*s=6

We move all terms to the left:

10/11*s-(6)=0


Domain of the equation: 11*s!=0

s!=0/1

s!=0

s∈R


We multiply all the terms by the denominator


-6*11*s+10=0

Wy multiply elements

-66s*s+10=0

Wy multiply elements

-66s^2+10=0

a = -66; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-66)·10
Δ = 2640
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:

$\sqrt{\Delta}=\sqrt{2640}=\sqrt{16*165}=\sqrt{16}*\sqrt{165}=4\sqrt{165}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{165}}{2*-66}=\frac{0-4\sqrt{165}}{-132}
=-\frac{4\sqrt{165}}{-132}
=-\frac{\sqrt{165}}{-33}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{165}}{2*-66}=\frac{0+4\sqrt{165}}{-132}
=\frac{4\sqrt{165}}{-132}
=\frac{\sqrt{165}}{-33}
$