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-6t^2+54t-120=0
a = -6; b = 54; c = -120;
Δ = b2-4ac
Δ = 542-4·(-6)·(-120)
Δ = 36
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{36}=6$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6}{2*-6}=\frac{-60}{-12} =+5 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6}{2*-6}=\frac{-48}{-12} =+4 $
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