0=0.8t^2-10t-2

Solution for 0=0.8t^2-10t-2 equation:

0=0.8t^2-10t-2

We move all terms to the left:

0-(0.8t^2-10t-2)=0

We add all the numbers together, and all the variables

-(0.8t^2-10t-2)=0

We get rid of parentheses

-0.8t^2+10t+2=0

a = -0.8; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·(-0.8)·2
Δ = 106.4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-\sqrt{106.4}}{2*-0.8}=\frac{-10-\sqrt{106.4}}{-1.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+\sqrt{106.4}}{2*-0.8}=\frac{-10+\sqrt{106.4}}{-1.6}
$