101=45t-5t2

Solution for 101=45t-5t2 equation:

101=45t-5t^2

We move all terms to the left:

101-(45t-5t^2)=0

We get rid of parentheses

5t^2-45t+101=0

a = 5; b = -45; c = +101;
Δ = b2-4ac
Δ = -452-4·5·101
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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