Whakaoti i te y=ax^2-(2a-3)x+(a-1)

$$y = a x ^ { 2 } - ( 2 a - 3 ) x + ( a - 1 )$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-\frac{3x-y-1}{\left(x-1\right)^{2}}\text{, }&x\neq 1\\a\in \mathrm{C}\text{, }&y=2\text{ and }x=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2a-3 ki te x.

$$y=ax^{2}-\left(2ax-3x\right)+a-1$$

Hei kimi i te tauaro o 2ax-3x, kimihia te tauaro o ia taurangi.

$$y=ax^{2}-2ax+3x+a-1$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax^{2}-2ax+3x+a-1=y$$

Tangohia te 3x mai i ngā taha e rua.

$$ax^{2}-2ax+a-1=y-3x$$

Me tāpiri te 1 ki ngā taha e rua.

$$ax^{2}-2ax+a=y-3x+1$$

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

$$\left(x^{2}-2x+1\right)a=y-3x+1$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}-2x+1\right)a=1+y-3x$$

Whakawehea ngā taha e rua ki te x^{2}-2x+1.

$$\frac{\left(x^{2}-2x+1\right)a}{x^{2}-2x+1}=\frac{1+y-3x}{x^{2}-2x+1}$$

Mā te whakawehe ki te x^{2}-2x+1 ka wetekia te whakareanga ki te x^{2}-2x+1.

$$a=\frac{1+y-3x}{x^{2}-2x+1}$$

Whakawehe y-3x+1 ki te x^{2}-2x+1.

$$a=\frac{1+y-3x}{\left(x-1\right)^{2}}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{3x-y-1}{\left(x-1\right)^{2}}\text{, }&x\neq 1\\a\in \mathrm{R}\text{, }&y=2\text{ and }x=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 2a-3 ki te x.

$$y=ax^{2}-\left(2ax-3x\right)+a-1$$

Hei kimi i te tauaro o 2ax-3x, kimihia te tauaro o ia taurangi.

$$y=ax^{2}-2ax+3x+a-1$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax^{2}-2ax+3x+a-1=y$$

Tangohia te 3x mai i ngā taha e rua.

$$ax^{2}-2ax+a-1=y-3x$$

Me tāpiri te 1 ki ngā taha e rua.

$$ax^{2}-2ax+a=y-3x+1$$

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

$$\left(x^{2}-2x+1\right)a=y-3x+1$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}-2x+1\right)a=1+y-3x$$

Whakawehea ngā taha e rua ki te x^{2}-2x+1.

$$\frac{\left(x^{2}-2x+1\right)a}{x^{2}-2x+1}=\frac{1+y-3x}{x^{2}-2x+1}$$

Mā te whakawehe ki te x^{2}-2x+1 ka wetekia te whakareanga ki te x^{2}-2x+1.

$$a=\frac{1+y-3x}{x^{2}-2x+1}$$

Whakawehe y-3x+1 ki te x^{2}-2x+1.

$$a=\frac{1+y-3x}{\left(x-1\right)^{2}}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4ay-8a+9}+2a-3}{2a}\text{; }x=\frac{-\sqrt{4ay-8a+9}+2a-3}{2a}\text{, }&a\neq 0\\x=\frac{y+1}{3}\text{, }&a=0\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{4ay-8a+9}+2a-3}{2a}\text{; }x=\frac{-\sqrt{4ay-8a+9}+2a-3}{2a}\text{, }&\left(a>0\text{ or }y\leq 2-\frac{9}{4a}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }a\neq 0\right)\text{ and }\left(a<0\text{ or }\left(a\neq 0\text{ and }y\geq 2-\frac{9}{4a}\right)\right)\\x=\frac{y+1}{3}\text{, }&a=0\end{matrix}\right.$$