(3s+6)(2s-1)=180

Solution for (3s+6)(2s-1)=180 equation:

(3s+6)(2s-1)=180

We move all terms to the left:

(3s+6)(2s-1)-(180)=0

We multiply parentheses ..

(+6s^2-3s+12s-6)-180=0

We get rid of parentheses

6s^2-3s+12s-6-180=0

We add all the numbers together, and all the variables

6s^2+9s-186=0

a = 6; b = 9; c = -186;
Δ = b2-4ac
Δ = 92-4·6·(-186)
Δ = 4545
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:

$\sqrt{\Delta}=\sqrt{4545}=\sqrt{9*505}=\sqrt{9}*\sqrt{505}=3\sqrt{505}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{505}}{2*6}=\frac{-9-3\sqrt{505}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{505}}{2*6}=\frac{-9+3\sqrt{505}}{12}
$