120=34t+2t^2

Solution for 120=34t+2t^2 equation:

120=34t+2t^2

We move all terms to the left:

120-(34t+2t^2)=0

We get rid of parentheses

-2t^2-34t+120=0

a = -2; b = -34; c = +120;
Δ = b2-4ac
Δ = -342-4·(-2)·120
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-46}{2*-2}=\frac{-12}{-4}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+46}{2*-2}=\frac{80}{-4}
=-20
$