3s(s-2)=128

Solution for 3s(s-2)=128 equation:

3s(s-2)=128

We move all terms to the left:

3s(s-2)-(128)=0

We multiply parentheses

3s^2-6s-128=0

a = 3; b = -6; c = -128;
Δ = b2-4ac
Δ = -62-4·3·(-128)
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{393}}{2*3}=\frac{6-2\sqrt{393}}{6}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{393}}{2*3}=\frac{6+2\sqrt{393}}{6}
$