Réitigh x:x^2+(3-2a)x-6a=0

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

Réitigh do a.

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

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi x^{2}.

$$x+\left(3-2a\right)xx^{2}-6ax^{2}=0$$

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 1 agus 2 chun 3 a bhaint amach.

$$x+\left(3-2a\right)x^{3}-6ax^{2}=0$$

Úsáid an t-airí dáileach chun 3-2a a mhéadú faoi x^{3}.

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

Bain x ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$3x^{3}-2ax^{3}-6ax^{2}=-x$$

Bain 3x^{3} ón dá thaobh.

$$-2ax^{3}-6ax^{2}=-x-3x^{3}$$

Comhcheangail na téarmaí ar fad ina bhfuil a.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi -2x^{3}-6x^{2}.

$$\frac{\left(-2x^{3}-6x^{2}\right)a}{-2x^{3}-6x^{2}}=-\frac{x\left(3x^{2}+1\right)}{-2x^{3}-6x^{2}}$$

Má roinntear é faoi -2x^{3}-6x^{2} cuirtear an iolrúchán faoi -2x^{3}-6x^{2} ar ceal.

$$a=-\frac{x\left(3x^{2}+1\right)}{-2x^{3}-6x^{2}}$$

Roinn -x\left(1+3x^{2}\right) faoi -2x^{3}-6x^{2}.

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

Réitigh do x. (complex solution)

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

Réitigh do x.

$$\left\{\begin{matrix}x=\frac{\sqrt{9a^{2}+2a-3}+3a}{3-2a}\text{; }x=\frac{-\sqrt{9a^{2}+2a-3}+3a}{3-2a}\text{, }&a\leq \frac{-2\sqrt{7}-1}{9}\text{ or }\left(a\neq \frac{3}{2}\text{ and }a\geq \frac{2\sqrt{7}-1}{9}\right)\\x=\frac{1}{9}\text{, }&a=\frac{3}{2}\end{matrix}\right.$$