9t^2-3t-9=0

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

9t^2-3t-9=0

a = 9; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·9·(-9)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{37}}{2*9}=\frac{3-3\sqrt{37}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{37}}{2*9}=\frac{3+3\sqrt{37}}{18}
$