S^3+8s^2+17s+10=0

Solution for S^3+8s^2+17s+10=0 equation:

^3+8S^2+17S+10=0

We add all the numbers together, and all the variables

8S^2+17S=0

a = 8; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·8·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*8}=\frac{-34}{16}
=-2+1/8
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*8}=\frac{0}{16}
=0
$