17s-10+3(2s+1)s=1

Solution for 17s-10+3(2s+1)s=1 equation:

17s-10+3(2s+1)s=1

We move all terms to the left:

17s-10+3(2s+1)s-(1)=0

We add all the numbers together, and all the variables

17s+3(2s+1)s-11=0

We multiply parentheses

6s^2+17s+3s-11=0

We add all the numbers together, and all the variables

6s^2+20s-11=0

a = 6; b = 20; c = -11;
Δ = b2-4ac
Δ = 202-4·6·(-11)
Δ = 664
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:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{166}}{2*6}=\frac{-20-2\sqrt{166}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{166}}{2*6}=\frac{-20+2\sqrt{166}}{12}
$