(t)=-16t^2+6t+12

Solution for (t)=-16t^2+6t+12 equation:

(t)=-16t^2+6t+12

We move all terms to the left:

(t)-(-16t^2+6t+12)=0

We get rid of parentheses

16t^2-6t+t-12=0

We add all the numbers together, and all the variables

16t^2-5t-12=0

a = 16; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·16·(-12)
Δ = 793
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{-(-5)-\sqrt{793}}{2*16}=\frac{5-\sqrt{793}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{793}}{2*16}=\frac{5+\sqrt{793}}{32}
$