-5t^2+80t+12=0

Solution for -5t^2+80t+12=0 equation:

-5t^2+80t+12=0

a = -5; b = 80; c = +12;
Δ = b2-4ac
Δ = 802-4·(-5)·12
Δ = 6640
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:

$\sqrt{\Delta}=\sqrt{6640}=\sqrt{16*415}=\sqrt{16}*\sqrt{415}=4\sqrt{415}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{415}}{2*-5}=\frac{-80-4\sqrt{415}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{415}}{2*-5}=\frac{-80+4\sqrt{415}}{-10}
$