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6t^2-54t+84=0
a = 6; b = -54; c = +84;
Δ = b2-4ac
Δ = -542-4·6·84
Δ = 900
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{900}=30$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-30}{2*6}=\frac{24}{12} =2 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+30}{2*6}=\frac{84}{12} =7 $
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