.25t^2-80t=2000

Solution for .25t^2-80t=2000 equation:

.25t^2-80t=2000

We move all terms to the left:

.25t^2-80t-(2000)=0

a = .25; b = -80; c = -2000;
Δ = b2-4ac
Δ = -802-4·.25·(-2000)
Δ = 8400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{21}}{2*.25}=\frac{80-20\sqrt{21}}{0.5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{21}}{2*.25}=\frac{80+20\sqrt{21}}{0.5}
$