t=-16t^2+64t+144

Solution for t=-16t^2+64t+144 equation:

t=-16t^2+64t+144

We move all terms to the left:

t-(-16t^2+64t+144)=0

We get rid of parentheses

16t^2-64t+t-144=0

We add all the numbers together, and all the variables

16t^2-63t-144=0

a = 16; b = -63; c = -144;
Δ = b2-4ac
Δ = -632-4·16·(-144)
Δ = 13185
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:

$\sqrt{\Delta}=\sqrt{13185}=\sqrt{9*1465}=\sqrt{9}*\sqrt{1465}=3\sqrt{1465}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{1465}}{2*16}=\frac{63-3\sqrt{1465}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{1465}}{2*16}=\frac{63+3\sqrt{1465}}{32}
$