Whakaoti i te (a+3)x^2-8ax-30=0

$$( a + 3 ) x ^ { 2 } - 8 a x - 30 = 0$$

Whakaoti mō a

$$a=-\frac{3\left(x^{2}-10\right)}{x\left(x-8\right)}$$

$$x\neq 8\text{ and }x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te a+3 ki te x^{2}.

$$ax^{2}+3x^{2}-8ax-30=0$$

Tangohia te 3x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$ax^{2}-8ax-30=-3x^{2}$$

Me tāpiri te 30 ki ngā taha e rua.

$$ax^{2}-8ax=-3x^{2}+30$$

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

$$\left(x^{2}-8x\right)a=-3x^{2}+30$$

He hanga arowhānui tō te whārite.

$$\left(x^{2}-8x\right)a=30-3x^{2}$$

Whakawehea ngā taha e rua ki te x^{2}-8x.

$$\frac{\left(x^{2}-8x\right)a}{x^{2}-8x}=\frac{30-3x^{2}}{x^{2}-8x}$$

Mā te whakawehe ki te x^{2}-8x ka wetekia te whakareanga ki te x^{2}-8x.

$$a=\frac{30-3x^{2}}{x^{2}-8x}$$

Whakawehe -3x^{2}+30 ki te x^{2}-8x.

$$a=\frac{3\left(10-x^{2}\right)}{x\left(x-8\right)}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(8a^{2}+15a+45\right)}+4a}{a+3}\text{; }x=\frac{-\sqrt{2\left(8a^{2}+15a+45\right)}+4a}{a+3}\text{, }&a\neq -3\\x=\frac{5}{4}\text{, }&a=-3\end{matrix}\right.$$