Whakaoti i te (-2-m)x^2-(3m+1)x+4=0

$$( - 2 - m ) x ^ { 2 } - ( 3 m + 1 ) x + 4 = 0$$

Whakaoti mō m

$$m=\frac{4-x-2x^{2}}{x\left(x+3\right)}$$

$$x\neq -3\text{ and }x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te -2-m ki te x^{2}.

$$-2x^{2}-mx^{2}-\left(3m+1\right)x+4=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3m+1 ki te x.

$$-2x^{2}-mx^{2}-\left(3mx+x\right)+4=0$$

Hei kimi i te tauaro o 3mx+x, kimihia te tauaro o ia taurangi.

$$-2x^{2}-mx^{2}-3mx-x+4=0$$

Me tāpiri te 2x^{2} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-mx^{2}-3mx-x+4=2x^{2}$$

Me tāpiri te x ki ngā taha e rua.

$$-mx^{2}-3mx+4=2x^{2}+x$$

Tangohia te 4 mai i ngā taha e rua.

$$-mx^{2}-3mx=2x^{2}+x-4$$

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

$$\left(-x^{2}-3x\right)m=2x^{2}+x-4$$

Whakawehea ngā taha e rua ki te -x^{2}-3x.

$$\frac{\left(-x^{2}-3x\right)m}{-x^{2}-3x}=\frac{2x^{2}+x-4}{-x^{2}-3x}$$

Mā te whakawehe ki te -x^{2}-3x ka wetekia te whakareanga ki te -x^{2}-3x.

$$m=\frac{2x^{2}+x-4}{-x^{2}-3x}$$

Whakawehe 2x^{2}+x-4 ki te -x^{2}-3x.

$$m=\frac{2x^{2}+x-4}{-x\left(x+3\right)}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=-\frac{\sqrt{9m^{2}+22m+33}+3m+1}{2\left(m+2\right)}\text{; }x=-\frac{-\sqrt{9m^{2}+22m+33}+3m+1}{2\left(m+2\right)}\text{, }&m\neq -2\\x=-\frac{4}{5}\text{, }&m=-2\end{matrix}\right.$$