Whakaoti i te 2x^2+(k-6)x-3k=0

$$2 x ^ { 2 } + ( k - 6 ) x - 3 k = 0$$

Whakaoti mō k (complex solution)

$$\left\{\begin{matrix}\\k=-2x\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=3\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te k-6 ki te x.

$$2x^{2}+kx-6x-3k=0$$

Tangohia te 2x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$kx-6x-3k=-2x^{2}$$

Me tāpiri te 6x ki ngā taha e rua.

$$kx-3k=-2x^{2}+6x$$

Pahekotia ngā kīanga tau katoa e whai ana i te k.

$$\left(x-3\right)k=-2x^{2}+6x$$

He hanga arowhānui tō te whārite.

$$\left(x-3\right)k=6x-2x^{2}$$

Whakawehea ngā taha e rua ki te -3+x.

$$\frac{\left(x-3\right)k}{x-3}=\frac{2x\left(3-x\right)}{x-3}$$

Mā te whakawehe ki te -3+x ka wetekia te whakareanga ki te -3+x.

$$k=\frac{2x\left(3-x\right)}{x-3}$$

Whakawehe 2x\left(3-x\right) ki te -3+x.

$$k=-2x$$

Whakaoti mō k

$$\left\{\begin{matrix}\\k=-2x\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=3\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te k-6 ki te x.

$$2x^{2}+kx-6x-3k=0$$

Tangohia te 2x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$kx-6x-3k=-2x^{2}$$

Me tāpiri te 6x ki ngā taha e rua.

$$kx-3k=-2x^{2}+6x$$

Pahekotia ngā kīanga tau katoa e whai ana i te k.

$$\left(x-3\right)k=-2x^{2}+6x$$

He hanga arowhānui tō te whārite.

$$\left(x-3\right)k=6x-2x^{2}$$

Whakawehea ngā taha e rua ki te -3+x.

$$\frac{\left(x-3\right)k}{x-3}=\frac{2x\left(3-x\right)}{x-3}$$

Mā te whakawehe ki te -3+x ka wetekia te whakareanga ki te -3+x.

$$k=\frac{2x\left(3-x\right)}{x-3}$$

Whakawehe 2x\left(3-x\right) ki te -3+x.

$$k=-2x$$

Whakaoti mō x

$$x=-\frac{k}{2}$$

$$x=3$$