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3t^2-8t-3=0
a = 3; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·3·(-3)
Δ = 100
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{100}=10$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*3}=\frac{-2}{6} =-1/3 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*3}=\frac{18}{6} =3 $
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