140=50t-2t^2

Solution for 140=50t-2t^2 equation:

140=50t-2t^2

We move all terms to the left:

140-(50t-2t^2)=0

We get rid of parentheses

2t^2-50t+140=0

a = 2; b = -50; c = +140;
Δ = b2-4ac
Δ = -502-4·2·140
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{345}}{2*2}=\frac{50-2\sqrt{345}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{345}}{2*2}=\frac{50+2\sqrt{345}}{4}
$