-3s(5s-3)-9=-2(9s+6)-2

Solution for -3s(5s-3)-9=-2(9s+6)-2 equation:

-3s(5s-3)-9=-2(9s+6)-2

We move all terms to the left:

-3s(5s-3)-9-(-2(9s+6)-2)=0

We multiply parentheses

-15s^2+9s-(-2(9s+6)-2)-9=0


We calculate terms in parentheses: -(-2(9s+6)-2), so:

-2(9s+6)-2

We multiply parentheses

-18s-12-2

We add all the numbers together, and all the variables

-18s-14

Back to the equation:

-(-18s-14)


We get rid of parentheses

-15s^2+9s+18s+14-9=0

We add all the numbers together, and all the variables

-15s^2+27s+5=0

a = -15; b = 27; c = +5;
Δ = b2-4ac
Δ = 272-4·(-15)·5
Δ = 1029
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:

$\sqrt{\Delta}=\sqrt{1029}=\sqrt{49*21}=\sqrt{49}*\sqrt{21}=7\sqrt{21}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-7\sqrt{21}}{2*-15}=\frac{-27-7\sqrt{21}}{-30}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+7\sqrt{21}}{2*-15}=\frac{-27+7\sqrt{21}}{-30}
$