-45=10t-5t^2

Solution for -45=10t-5t^2 equation:

-45=10t-5t^2

We move all terms to the left:

-45-(10t-5t^2)=0

We get rid of parentheses

5t^2-10t-45=0

a = 5; b = -10; c = -45;
Δ = b2-4ac
Δ = -102-4·5·(-45)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{10}}{2*5}=\frac{10-10\sqrt{10}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{10}}{2*5}=\frac{10+10\sqrt{10}}{10}
$