120=150+49t-9t^2

Solution for 120=150+49t-9t^2 equation:

120=150+49t-9t^2

We move all terms to the left:

120-(150+49t-9t^2)=0

We get rid of parentheses

9t^2-49t-150+120=0

We add all the numbers together, and all the variables

9t^2-49t-30=0

a = 9; b = -49; c = -30;
Δ = b2-4ac
Δ = -492-4·9·(-30)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-59}{2*9}=\frac{-10}{18}
=-5/9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+59}{2*9}=\frac{108}{18}
=6
$