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17=7+27t+-16t^2
We move all terms to the left:
17-(7+27t+-16t^2)=0
We use the square of the difference formula
-(7+27t-16t^2)+17=0
We get rid of parentheses
16t^2-27t-7+17=0
We add all the numbers together, and all the variables
16t^2-27t+10=0
a = 16; b = -27; c = +10;
Δ = b2-4ac
Δ = -272-4·16·10
Δ = 89
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{-(-27)-\sqrt{89}}{2*16}=\frac{27-\sqrt{89}}{32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{89}}{2*16}=\frac{27+\sqrt{89}}{32} $
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