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3x^{2}+5x+1=0
Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.
x=\frac{-5±\sqrt{5^{2}-4\times 3}}{2\times 3}
Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.
x=\frac{-5±\sqrt{25-4\times 3}}{2\times 3}
Pūrua 5.
x=\frac{-5±\sqrt{25-12}}{2\times 3}
Whakareatia -4 ki te 3.
x=\frac{-5±\sqrt{13}}{2\times 3}
Tāpiri 25 ki te -12.
x=\frac{-5±\sqrt{13}}{6}
Whakareatia 2 ki te 3.
x=\frac{\sqrt{13}-5}{6}
Nā, me whakaoti te whārite x=\frac{-5±\sqrt{13}}{6} ina he tāpiri te ±. Tāpiri -5 ki te \sqrt{13}.
x=\frac{-\sqrt{13}-5}{6}
Nā, me whakaoti te whārite x=\frac{-5±\sqrt{13}}{6} ina he tango te ±. Tango \sqrt{13} mai i -5.
3x^{2}+5x+1=3\left(x-\frac{\sqrt{13}-5}{6}\right)\left(x-\frac{-\sqrt{13}-5}{6}\right)
Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{-5+\sqrt{13}}{6} mō te x_{1} me te \frac{-5-\sqrt{13}}{6} mō te x_{2}.