50=35t-5t2

Solution for 50=35t-5t2 equation:

50=35t-5t^2

We move all terms to the left:

50-(35t-5t^2)=0

We get rid of parentheses

5t^2-35t+50=0

a = 5; b = -35; c = +50;
Δ = b2-4ac
Δ = -352-4·5·50
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-15}{2*5}=\frac{20}{10}
=2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+15}{2*5}=\frac{50}{10}
=5
$