(0.29t^2)+42t-72.9=0

Solution for (0.29t^2)+42t-72.9=0 equation:

(0.29t^2)+42t-72.9=0

We add all the numbers together, and all the variables

42t+(0.29t^2)-72.9=0

We get rid of parentheses

0.29t^2+42t-72.9=0

a = 0.29; b = 42; c = -72.9;
Δ = b2-4ac
Δ = 422-4·0.29·(-72.9)
Δ = 1848.564
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{-(42)-\sqrt{1848.564}}{2*0.29}=\frac{-42-\sqrt{1848.564}}{0.58}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+\sqrt{1848.564}}{2*0.29}=\frac{-42+\sqrt{1848.564}}{0.58}
$