0=20+20t-12t2

Solution for 0=20+20t-12t2 equation:

0=20+20t-12t^2

We move all terms to the left:

0-(20+20t-12t^2)=0

We add all the numbers together, and all the variables

-(20+20t-12t^2)=0

We get rid of parentheses

12t^2-20t-20=0

a = 12; b = -20; c = -20;
Δ = b2-4ac
Δ = -202-4·12·(-20)
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{85}}{2*12}=\frac{20-4\sqrt{85}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{85}}{2*12}=\frac{20+4\sqrt{85}}{24}
$