-16t^2+30t=-6

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

-16t^2+30t=-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -16; b = 30; c = +6;
Δ = b2-4ac
Δ = 302-4·(-16)·6
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{321}}{2*-16}=\frac{-30-2\sqrt{321}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{321}}{2*-16}=\frac{-30+2\sqrt{321}}{-32}
$