9t^2-2t-1/3=0

Solution for 9t^2-2t-1/3=0 equation:

9t^2-2t-1/3=0

We multiply all the terms by the denominator


9t^2*3-2t*3-1=0

Wy multiply elements

27t^2-6t-1=0

a = 27; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·27·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*27}=\frac{-6}{54}
=-1/9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*27}=\frac{18}{54}
=1/3
$