50t-2t^2=140

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

50t-2t^2=140

We move all terms to the left:

50t-2t^2-(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}
$