0=5-6t+0.83t^2

Solution for 0=5-6t+0.83t^2 equation:

0=5-6t+0.83t^2

We move all terms to the left:

0-(5-6t+0.83t^2)=0

We add all the numbers together, and all the variables

-(5-6t+0.83t^2)=0

We get rid of parentheses

-0.83t^2+6t-5=0

a = -0.83; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·(-0.83)·(-5)
Δ = 19.4
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{-(6)-\sqrt{19.4}}{2*-0.83}=\frac{-6-\sqrt{19.4}}{-1.66}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+\sqrt{19.4}}{2*-0.83}=\frac{-6+\sqrt{19.4}}{-1.66}
$