13=3+30t-5t^2

Solution for 13=3+30t-5t^2 equation:

13=3+30t-5t^2

We move all terms to the left:

13-(3+30t-5t^2)=0

We get rid of parentheses

5t^2-30t-3+13=0

We add all the numbers together, and all the variables

5t^2-30t+10=0

a = 5; b = -30; c = +10;
Δ = b2-4ac
Δ = -302-4·5·10
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{7}}{2*5}=\frac{30-10\sqrt{7}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{7}}{2*5}=\frac{30+10\sqrt{7}}{10}
$