0.6=8t+5t2

Solution for 0.6=8t+5t2 equation:

0.6=8t+5t^2

We move all terms to the left:

0.6-(8t+5t^2)=0

We get rid of parentheses

-5t^2-8t+0.6=0

a = -5; b = -8; c = +0.6;
Δ = b2-4ac
Δ = -82-4·(-5)·0.6
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{19}}{2*-5}=\frac{8-2\sqrt{19}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{19}}{2*-5}=\frac{8+2\sqrt{19}}{-10}
$