-12t^2+480t+30=3000

Solution for -12t^2+480t+30=3000 equation:

-12t^2+480t+30=3000

We move all terms to the left:

-12t^2+480t+30-(3000)=0

We add all the numbers together, and all the variables

-12t^2+480t-2970=0

a = -12; b = 480; c = -2970;
Δ = b2-4ac
Δ = 4802-4·(-12)·(-2970)
Δ = 87840
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:

$\sqrt{\Delta}=\sqrt{87840}=\sqrt{144*610}=\sqrt{144}*\sqrt{610}=12\sqrt{610}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-12\sqrt{610}}{2*-12}=\frac{-480-12\sqrt{610}}{-24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+12\sqrt{610}}{2*-12}=\frac{-480+12\sqrt{610}}{-24}
$