30t-2t^2=56.25

Solution for 30t-2t^2=56.25 equation:

30t-2t^2=56.25

We move all terms to the left:

30t-2t^2-(56.25)=0

We add all the numbers together, and all the variables

-2t^2+30t-56.25=0

a = -2; b = 30; c = -56.25;
Δ = b2-4ac
Δ = 302-4·(-2)·(-56.25)
Δ = 450
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:

$\sqrt{\Delta}=\sqrt{450}=\sqrt{225*2}=\sqrt{225}*\sqrt{2}=15\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-15\sqrt{2}}{2*-2}=\frac{-30-15\sqrt{2}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+15\sqrt{2}}{2*-2}=\frac{-30+15\sqrt{2}}{-4}
$