164=-16t^2+138t+120

Solution for 164=-16t^2+138t+120 equation:

164=-16t^2+138t+120

We move all terms to the left:

164-(-16t^2+138t+120)=0

We get rid of parentheses

16t^2-138t-120+164=0

We add all the numbers together, and all the variables

16t^2-138t+44=0

a = 16; b = -138; c = +44;
Δ = b2-4ac
Δ = -1382-4·16·44
Δ = 16228
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:

$\sqrt{\Delta}=\sqrt{16228}=\sqrt{4*4057}=\sqrt{4}*\sqrt{4057}=2\sqrt{4057}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{4057}}{2*16}=\frac{138-2\sqrt{4057}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{4057}}{2*16}=\frac{138+2\sqrt{4057}}{32}
$