9(-6-5s)s=6

Solution for 9(-6-5s)s=6 equation:

9(-6-5s)s=6

We move all terms to the left:

9(-6-5s)s-(6)=0

We add all the numbers together, and all the variables

9(-5s-6)s-6=0

We multiply parentheses

-45s^2-54s-6=0

a = -45; b = -54; c = -6;
Δ = b2-4ac
Δ = -542-4·(-45)·(-6)
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{51}}{2*-45}=\frac{54-6\sqrt{51}}{-90}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{51}}{2*-45}=\frac{54+6\sqrt{51}}{-90}
$