105=50t-5t^2

Solution for 105=50t-5t^2 equation:

105=50t-5t^2

We move all terms to the left:

105-(50t-5t^2)=0

We get rid of parentheses

5t^2-50t+105=0

a = 5; b = -50; c = +105;
Δ = b2-4ac
Δ = -502-4·5·105
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-20}{2*5}=\frac{30}{10}
=3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20}{2*5}=\frac{70}{10}
=7
$