20=16t^2+146t

Solution for 20=16t^2+146t equation:

20=16t^2+146t

We move all terms to the left:

20-(16t^2+146t)=0

We get rid of parentheses

-16t^2-146t+20=0

a = -16; b = -146; c = +20;
Δ = b2-4ac
Δ = -1462-4·(-16)·20
Δ = 22596
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:

$\sqrt{\Delta}=\sqrt{22596}=\sqrt{4*5649}=\sqrt{4}*\sqrt{5649}=2\sqrt{5649}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-146)-2\sqrt{5649}}{2*-16}=\frac{146-2\sqrt{5649}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-146)+2\sqrt{5649}}{2*-16}=\frac{146+2\sqrt{5649}}{-32}
$