50=0.005s^2+0.007s-0.031

Solution for 50=0.005s^2+0.007s-0.031 equation:

50=0.005s^2+0.007s-0.031

We move all terms to the left:

50-(0.005s^2+0.007s-0.031)=0

We get rid of parentheses

-0.005s^2-0.007s+0.031+50=0

We add all the numbers together, and all the variables

-0.005s^2-0.007s+50.031=0

a = -0.005; b = -0.007; c = +50.031;
Δ = b2-4ac
Δ = -0.0072-4·(-0.005)·50.031
Δ = 1.000669
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{-(-0.007)-\sqrt{1.000669}}{2*-0.005}=\frac{0.007-\sqrt{1.000669}}{-0.01}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.007)+\sqrt{1.000669}}{2*-0.005}=\frac{0.007+\sqrt{1.000669}}{-0.01}
$