Whakaoti i te 06t-160/3*5*10^-4/4*10^-3t^2=-204

$$06 t - \frac { \frac { 160 } { 3 } \times 5 \times 10 ^ { - 4 } } { 4 \times 10 ^ { - 3 } } t ^ { 2 } = - 204$$

Whakaoti mō t

$$t = \frac{3 \sqrt{85}}{5} \approx 5.531726674$$

$$t = -\frac{3 \sqrt{85}}{5} \approx -5.531726674$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 0 ki te 6, ka 0.

$$0t-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$0-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te taurunga i te taupū o te tauraro.

$$0-\frac{5\times \frac{160}{3}}{4\times 10^{1}}t^{2}=-204$$

Whakareatia te 5 ki te \frac{160}{3}, ka \frac{800}{3}.

$$0-\frac{\frac{800}{3}}{4\times 10^{1}}t^{2}=-204$$

Tātaihia te 10 mā te pū o 1, kia riro ko 10.

$$0-\frac{\frac{800}{3}}{4\times 10}t^{2}=-204$$

Whakareatia te 4 ki te 10, ka 40.

$$0-\frac{\frac{800}{3}}{40}t^{2}=-204$$

Tuhia te \frac{\frac{800}{3}}{40} hei hautanga kotahi.

$$0-\frac{800}{3\times 40}t^{2}=-204$$

Whakareatia te 3 ki te 40, ka 120.

$$0-\frac{800}{120}t^{2}=-204$$

Whakahekea te hautanga \frac{800}{120} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$0-\frac{20}{3}t^{2}=-204$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$-\frac{20}{3}t^{2}=-204$$

Me whakarea ngā taha e rua ki te -\frac{3}{20}, te tau utu o -\frac{20}{3}.

$$t^{2}=-204\left(-\frac{3}{20}\right)$$

Whakareatia te -204 ki te -\frac{3}{20}, ka \frac{153}{5}.

$$t^{2}=\frac{153}{5}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$t=\frac{3\sqrt{85}}{5} t=-\frac{3\sqrt{85}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 6, ka 0.

$$0t-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$0-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te taurunga i te taupū o te tauraro.

$$0-\frac{5\times \frac{160}{3}}{4\times 10^{1}}t^{2}=-204$$

Whakareatia te 5 ki te \frac{160}{3}, ka \frac{800}{3}.

$$0-\frac{\frac{800}{3}}{4\times 10^{1}}t^{2}=-204$$

Tātaihia te 10 mā te pū o 1, kia riro ko 10.

$$0-\frac{\frac{800}{3}}{4\times 10}t^{2}=-204$$

Whakareatia te 4 ki te 10, ka 40.

$$0-\frac{\frac{800}{3}}{40}t^{2}=-204$$

Tuhia te \frac{\frac{800}{3}}{40} hei hautanga kotahi.

$$0-\frac{800}{3\times 40}t^{2}=-204$$

Whakareatia te 3 ki te 40, ka 120.

$$0-\frac{800}{120}t^{2}=-204$$

Whakahekea te hautanga \frac{800}{120} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$0-\frac{20}{3}t^{2}=-204$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$-\frac{20}{3}t^{2}=-204$$

Me tāpiri te 204 ki ngā taha e rua.

$$-\frac{20}{3}t^{2}+204=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -\frac{20}{3} mō a, 0 mō b, me 204 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{20}{3}\right)\times 204}}{2\left(-\frac{20}{3}\right)}$$

Pūrua 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{20}{3}\right)\times 204}}{2\left(-\frac{20}{3}\right)}$$

Whakareatia -4 ki te -\frac{20}{3}.

$$t=\frac{0±\sqrt{\frac{80}{3}\times 204}}{2\left(-\frac{20}{3}\right)}$$

Whakareatia \frac{80}{3} ki te 204.

$$t=\frac{0±\sqrt{5440}}{2\left(-\frac{20}{3}\right)}$$

Tuhia te pūtakerua o te 5440.

$$t=\frac{0±8\sqrt{85}}{2\left(-\frac{20}{3}\right)}$$

Whakareatia 2 ki te -\frac{20}{3}.

$$t=\frac{0±8\sqrt{85}}{-\frac{40}{3}}$$

Nā, me whakaoti te whārite t=\frac{0±8\sqrt{85}}{-\frac{40}{3}} ina he tāpiri te ±.

$$t=-\frac{3\sqrt{85}}{5}$$

Nā, me whakaoti te whārite t=\frac{0±8\sqrt{85}}{-\frac{40}{3}} ina he tango te ±.

$$t=\frac{3\sqrt{85}}{5}$$

Kua oti te whārite te whakatau.

$$t=-\frac{3\sqrt{85}}{5} t=\frac{3\sqrt{85}}{5}$$