t=-16t^2+35t+1.5

Solution for t=-16t^2+35t+1.5 equation:

t=-16t^2+35t+1.5

We move all terms to the left:

t-(-16t^2+35t+1.5)=0

We get rid of parentheses

16t^2-35t+t-1.5=0

We add all the numbers together, and all the variables

16t^2-34t-1.5=0

a = 16; b = -34; c = -1.5;
Δ = b2-4ac
Δ = -342-4·16·(-1.5)
Δ = 1252
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:

$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{313}}{2*16}=\frac{34-2\sqrt{313}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{313}}{2*16}=\frac{34+2\sqrt{313}}{32}
$