50=80t-5t^2

Solution for 50=80t-5t^2 equation:

50=80t-5t^2

We move all terms to the left:

50-(80t-5t^2)=0

We get rid of parentheses

5t^2-80t+50=0

a = 5; b = -80; c = +50;
Δ = b2-4ac
Δ = -802-4·5·50
Δ = 5400
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:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-30\sqrt{6}}{2*5}=\frac{80-30\sqrt{6}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+30\sqrt{6}}{2*5}=\frac{80+30\sqrt{6}}{10}
$