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2x^{2}+2x-3=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{-2±\sqrt{2^{2}-4\times 2\left(-3\right)}}{2\times 2}
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{-2±\sqrt{4-4\times 2\left(-3\right)}}{2\times 2}
Pūrua 2.
x=\frac{-2±\sqrt{4-8\left(-3\right)}}{2\times 2}
Whakareatia -4 ki te 2.
x=\frac{-2±\sqrt{4+24}}{2\times 2}
Whakareatia -8 ki te -3.
x=\frac{-2±\sqrt{28}}{2\times 2}
Tāpiri 4 ki te 24.
x=\frac{-2±2\sqrt{7}}{2\times 2}
Tuhia te pūtakerua o te 28.
x=\frac{-2±2\sqrt{7}}{4}
Whakareatia 2 ki te 2.
x=\frac{2\sqrt{7}-2}{4}
Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{7}}{4} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{7}.
x=\frac{\sqrt{7}-1}{2}
Whakawehe -2+2\sqrt{7} ki te 4.
x=\frac{-2\sqrt{7}-2}{4}
Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{7}}{4} ina he tango te ±. Tango 2\sqrt{7} mai i -2.
x=\frac{-\sqrt{7}-1}{2}
Whakawehe -2-2\sqrt{7} ki te 4.
2x^{2}+2x-3=2\left(x-\frac{\sqrt{7}-1}{2}\right)\left(x-\frac{-\sqrt{7}-1}{2}\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{-1+\sqrt{7}}{2} mō te x_{1} me te \frac{-1-\sqrt{7}}{2} mō te x_{2}.