0=5t^2-2t-0.2

Solution for 0=5t^2-2t-0.2 equation:

0=5t^2-2t-0.2

We move all terms to the left:

0-(5t^2-2t-0.2)=0

We add all the numbers together, and all the variables

-(5t^2-2t-0.2)=0

We get rid of parentheses

-5t^2+2t+0.2=0

a = -5; b = 2; c = +0.2;
Δ = b2-4ac
Δ = 22-4·(-5)·0.2
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2}}{2*-5}=\frac{-2-2\sqrt{2}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2}}{2*-5}=\frac{-2+2\sqrt{2}}{-10}
$