274800=-0.01t^2+136t-120000

Solution for 274800=-0.01t^2+136t-120000 equation:

274800=-0.01t^2+136t-120000

We move all terms to the left:

274800-(-0.01t^2+136t-120000)=0

We get rid of parentheses

0.01t^2-136t+120000+274800=0

We add all the numbers together, and all the variables

0.01t^2-136t+394800=0

a = 0.01; b = -136; c = +394800;
Δ = b2-4ac
Δ = -1362-4·0.01·394800
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-52}{2*0.01}=\frac{84}{0.02}
=4200
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+52}{2*0.01}=\frac{188}{0.02}
=9400
$