8000=-20s^2+1400s-12000

Solution for 8000=-20s^2+1400s-12000 equation:

8000=-20s^2+1400s-12000

We move all terms to the left:

8000-(-20s^2+1400s-12000)=0

We get rid of parentheses

20s^2-1400s+12000+8000=0

We add all the numbers together, and all the variables

20s^2-1400s+20000=0

a = 20; b = -1400; c = +20000;
Δ = b2-4ac
Δ = -14002-4·20·20000
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1400)-600}{2*20}=\frac{800}{40}
=20
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1400)+600}{2*20}=\frac{2000}{40}
=50
$