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-2.4=5.14t+-5t^2
We move all terms to the left:
-2.4-(5.14t+-5t^2)=0
We use the square of the difference formula
-(5.14t-5t^2)-2.4=0
We get rid of parentheses
5t^2-5.14t-2.4=0
a = 5; b = -5.14; c = -2.4;
Δ = b2-4ac
Δ = -5.142-4·5·(-2.4)
Δ = 74.4196
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{-(-5.14)-\sqrt{74.4196}}{2*5}=\frac{5.14-\sqrt{74.4196}}{10} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.14)+\sqrt{74.4196}}{2*5}=\frac{5.14+\sqrt{74.4196}}{10} $
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