0=s^2+17s+15

Solution for 0=s^2+17s+15 equation:

0=s^2+17s+15

We move all terms to the left:

0-(s^2+17s+15)=0

We add all the numbers together, and all the variables

-(s^2+17s+15)=0

We get rid of parentheses

-s^2-17s-15=0

We add all the numbers together, and all the variables

-1s^2-17s-15=0

a = -1; b = -17; c = -15;
Δ = b2-4ac
Δ = -172-4·(-1)·(-15)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{229}}{2*-1}=\frac{17-\sqrt{229}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{229}}{2*-1}=\frac{17+\sqrt{229}}{-2}
$