Whakaoti i te ax^2+6x-1=0

$$a x ^ { 2 } + 6 x - 1 = 0$$

Whakaoti mō a

$$a=\frac{1-6x}{x^{2}}$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 6x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$ax^{2}-1=-6x$$

Me tāpiri te 1 ki ngā taha e rua.

$$ax^{2}=-6x+1$$

He hanga arowhānui tō te whārite.

$$x^{2}a=1-6x$$

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

$$\frac{x^{2}a}{x^{2}}=\frac{1-6x}{x^{2}}$$

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

$$a=\frac{1-6x}{x^{2}}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{a+9}-3}{a}\text{; }x=-\frac{\sqrt{a+9}+3}{a}\text{, }&a\neq 0\\x=\frac{1}{6}\text{, }&a=0\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{a+9}-3}{a}\text{; }x=-\frac{\sqrt{a+9}+3}{a}\text{, }&a\neq 0\text{ and }a\geq -9\\x=\frac{1}{6}\text{, }&a=0\end{matrix}\right.$$