50=50+45t-5t^2

Solution for 50=50+45t-5t^2 equation:

50=50+45t-5t^2

We move all terms to the left:

50-(50+45t-5t^2)=0

We get rid of parentheses

5t^2-45t-50+50=0

We add all the numbers together, and all the variables

5t^2-45t=0

a = 5; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·5·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*5}=\frac{90}{10}
=9
$