5=65t-5t^2

Solution for 5=65t-5t^2 equation:

5=65t-5t^2

We move all terms to the left:

5-(65t-5t^2)=0

We get rid of parentheses

5t^2-65t+5=0

a = 5; b = -65; c = +5;
Δ = b2-4ac
Δ = -652-4·5·5
Δ = 4125
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:

$\sqrt{\Delta}=\sqrt{4125}=\sqrt{25*165}=\sqrt{25}*\sqrt{165}=5\sqrt{165}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{165}}{2*5}=\frac{65-5\sqrt{165}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{165}}{2*5}=\frac{65+5\sqrt{165}}{10}
$