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6t^2-21t-97=0
a = 6; b = -21; c = -97;
Δ = b2-4ac
Δ = -212-4·6·(-97)
Δ = 2769
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{-(-21)-\sqrt{2769}}{2*6}=\frac{21-\sqrt{2769}}{12} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{2769}}{2*6}=\frac{21+\sqrt{2769}}{12} $
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