-12=-16t^2+15t

Solution for -12=-16t^2+15t equation:

-12=-16t^2+15t

We move all terms to the left:

-12-(-16t^2+15t)=0

We get rid of parentheses

16t^2-15t-12=0

a = 16; b = -15; c = -12;
Δ = b2-4ac
Δ = -152-4·16·(-12)
Δ = 993
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{-(-15)-\sqrt{993}}{2*16}=\frac{15-\sqrt{993}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{993}}{2*16}=\frac{15+\sqrt{993}}{32}
$