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-16t^2+185t+17=0
a = -16; b = 185; c = +17;
Δ = b2-4ac
Δ = 1852-4·(-16)·17
Δ = 35313
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{-(185)-\sqrt{35313}}{2*-16}=\frac{-185-\sqrt{35313}}{-32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(185)+\sqrt{35313}}{2*-16}=\frac{-185+\sqrt{35313}}{-32} $
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