5=0.8t+5t^2

Solution for 5=0.8t+5t^2 equation:

5=0.8t+5t^2

We move all terms to the left:

5-(0.8t+5t^2)=0

We get rid of parentheses

-5t^2-0.8t+5=0

a = -5; b = -0.8; c = +5;
Δ = b2-4ac
Δ = -0.82-4·(-5)·5
Δ = 100.64
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{-(-0.8)-\sqrt{100.64}}{2*-5}=\frac{0.8-\sqrt{100.64}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{100.64}}{2*-5}=\frac{0.8+\sqrt{100.64}}{-10}
$