s(5/3+14)=26

Solution for s(5/3+14)=26 equation:

s(5/3+14)=26

We move all terms to the left:

s(5/3+14)-(26)=0

We multiply parentheses

5s^2+14s-26=0

a = 5; b = 14; c = -26;
Δ = b2-4ac
Δ = 142-4·5·(-26)
Δ = 716
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:

$\sqrt{\Delta}=\sqrt{716}=\sqrt{4*179}=\sqrt{4}*\sqrt{179}=2\sqrt{179}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{179}}{2*5}=\frac{-14-2\sqrt{179}}{10}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{179}}{2*5}=\frac{-14+2\sqrt{179}}{10}
$