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

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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} $

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