5s^2-17s=6=0

Solution for 5s^2-17s=6=0 equation:

5s^2-17s=6=0

We move all terms to the left:

5s^2-17s-(6)=0

a = 5; b = -17; c = -6;
Δ = b2-4ac
Δ = -172-4·5·(-6)
Δ = 409
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{409}}{2*5}=\frac{17-\sqrt{409}}{10}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{409}}{2*5}=\frac{17+\sqrt{409}}{10}
$