145=16t^2+16t

Solution for 145=16t^2+16t equation:

145=16t^2+16t

We move all terms to the left:

145-(16t^2+16t)=0

We get rid of parentheses

-16t^2-16t+145=0

a = -16; b = -16; c = +145;
Δ = b2-4ac
Δ = -162-4·(-16)·145
Δ = 9536
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:

$\sqrt{\Delta}=\sqrt{9536}=\sqrt{64*149}=\sqrt{64}*\sqrt{149}=8\sqrt{149}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{149}}{2*-16}=\frac{16-8\sqrt{149}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{149}}{2*-16}=\frac{16+8\sqrt{149}}{-32}
$