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100=2.16t^2-20.53t+54

We move all terms to the left:

100-(2.16t^2-20.53t+54)=0

We get rid of parentheses

-2.16t^2+20.53t-54+100=0

We add all the numbers together, and all the variables

-2.16t^2+20.53t+46=0

a = -2.16; b = 20.53; c = +46;

Δ = b^{2}-4ac

Δ = 20.53^{2}-4·(-2.16)·46

Δ = 818.9209

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{-(20.53)-\sqrt{818.9209}}{2*-2.16}=\frac{-20.53-\sqrt{818.9209}}{-4.32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20.53)+\sqrt{818.9209}}{2*-2.16}=\frac{-20.53+\sqrt{818.9209}}{-4.32} $

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