30t=2.5t^2+50

Solution for 30t=2.5t^2+50 equation:

30t=2.5t^2+50

We move all terms to the left:

30t-(2.5t^2+50)=0

We get rid of parentheses

-2.5t^2+30t-50=0

a = -2.5; b = 30; c = -50;
Δ = b2-4ac
Δ = 302-4·(-2.5)·(-50)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-20}{2*-2.5}=\frac{-50}{-5}
=+10
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+20}{2*-2.5}=\frac{-10}{-5}
=+2
$