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6t^2-47t-8=0
a = 6; b = -47; c = -8;
Δ = b2-4ac
Δ = -472-4·6·(-8)
Δ = 2401
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{2401}=49$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-49}{2*6}=\frac{-2}{12} =-1/6 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+49}{2*6}=\frac{96}{12} =8 $
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