0=-12t^2+80t+10

Solution for 0=-12t^2+80t+10 equation:

0=-12t^2+80t+10

We move all terms to the left:

0-(-12t^2+80t+10)=0

We add all the numbers together, and all the variables

-(-12t^2+80t+10)=0

We get rid of parentheses

12t^2-80t-10=0

a = 12; b = -80; c = -10;
Δ = b2-4ac
Δ = -802-4·12·(-10)
Δ = 6880
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:

$\sqrt{\Delta}=\sqrt{6880}=\sqrt{16*430}=\sqrt{16}*\sqrt{430}=4\sqrt{430}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{430}}{2*12}=\frac{80-4\sqrt{430}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{430}}{2*12}=\frac{80+4\sqrt{430}}{24}
$