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

Solution for 0=-5t^2+30t+3 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5t^2-30t-3=0

a = 5; b = -30; c = -3;
Δ = b2-4ac
Δ = -302-4·5·(-3)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{15}}{2*5}=\frac{30-8\sqrt{15}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{15}}{2*5}=\frac{30+8\sqrt{15}}{10}
$