60=3t+2t^2

Solution for 60=3t+2t^2 equation:

60=3t+2t^2

We move all terms to the left:

60-(3t+2t^2)=0

We get rid of parentheses

-2t^2-3t+60=0

a = -2; b = -3; c = +60;
Δ = b2-4ac
Δ = -32-4·(-2)·60
Δ = 489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{489}}{2*-2}=\frac{3-\sqrt{489}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{489}}{2*-2}=\frac{3+\sqrt{489}}{-4}
$