6+30t-16t^2=t

Solution for 6+30t-16t^2=t equation:

6+30t-16t^2=t

We move all terms to the left:

6+30t-16t^2-(t)=0

We add all the numbers together, and all the variables

-16t^2+29t+6=0

a = -16; b = 29; c = +6;
Δ = b2-4ac
Δ = 292-4·(-16)·6
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-35}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+35}{2*-16}=\frac{6}{-32}
=-3/16
$