12.3t^2-8t-33=0

Solution for 12.3t^2-8t-33=0 equation:

12.3t^2-8t-33=0

a = 12.3; b = -8; c = -33;
Δ = b2-4ac
Δ = -82-4·12.3·(-33)
Δ = 1687.6
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{-(-8)-\sqrt{1687.6}}{2*12.3}=\frac{8-\sqrt{1687.6}}{24.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+\sqrt{1687.6}}{2*12.3}=\frac{8+\sqrt{1687.6}}{24.6}
$