0=20t-5t^2+1

Solution for 0=20t-5t^2+1 equation:

0=20t-5t^2+1

We move all terms to the left:

0-(20t-5t^2+1)=0

We add all the numbers together, and all the variables

-(20t-5t^2+1)=0

We get rid of parentheses

5t^2-20t-1=0

a = 5; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·5·(-1)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{105}}{2*5}=\frac{20-2\sqrt{105}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{105}}{2*5}=\frac{20+2\sqrt{105}}{10}
$