0.602=12.71t+-4.91t^2

Solution for 0.602=12.71t+-4.91t^2 equation:

0.602=12.71t+-4.91t^2

We move all terms to the left:

0.602-(12.71t+-4.91t^2)=0

We use the square of the difference formula

-(12.71t-4.91t^2)+0.602=0

We get rid of parentheses

4.91t^2-12.71t+0.602=0

a = 4.91; b = -12.71; c = +0.602;
Δ = b2-4ac
Δ = -12.712-4·4.91·0.602
Δ = 149.72082
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{-(-12.71)-\sqrt{149.72082}}{2*4.91}=\frac{12.71-\sqrt{149.72082}}{9.82}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.71)+\sqrt{149.72082}}{2*4.91}=\frac{12.71+\sqrt{149.72082}}{9.82}
$