-30+65t-5t^2=0

Solution for -30+65t-5t^2=0 equation:

-30+65t-5t^2=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}
$