30=65t-5t^2

Solution for 30=65t-5t^2 equation:

30=65t-5t^2

We move all terms to the left:

30-(65t-5t^2)=0

We get rid of parentheses

5t^2-65t+30=0

a = 5; b = -65; c = +30;
Δ = b2-4ac
Δ = -652-4·5·30
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{145}}{2*5}=\frac{65-5\sqrt{145}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{145}}{2*5}=\frac{65+5\sqrt{145}}{10}
$