30=-4s^2+40s+8

Solution for 30=-4s^2+40s+8 equation:

30=-4s^2+40s+8

We move all terms to the left:

30-(-4s^2+40s+8)=0

We get rid of parentheses

4s^2-40s-8+30=0

We add all the numbers together, and all the variables

4s^2-40s+22=0

a = 4; b = -40; c = +22;
Δ = b2-4ac
Δ = -402-4·4·22
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{78}}{2*4}=\frac{40-4\sqrt{78}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{78}}{2*4}=\frac{40+4\sqrt{78}}{8}
$