3+31t-16t^2=17

Solution for 3+31t-16t^2=17 equation:

3+31t-16t^2=17

We move all terms to the left:

3+31t-16t^2-(17)=0

We add all the numbers together, and all the variables

-16t^2+31t-14=0

a = -16; b = 31; c = -14;
Δ = b2-4ac
Δ = 312-4·(-16)·(-14)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{65}}{2*-16}=\frac{-31-\sqrt{65}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{65}}{2*-16}=\frac{-31+\sqrt{65}}{-32}
$