Issolvi y=3(ax^2+x)

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

Solvi għal a (complex solution)

$$\left\{\begin{matrix}a=\frac{y-3x}{3x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 3 b'ax^{2}+x.

$$y=3ax^{2}+3x$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$3ax^{2}+3x=y$$

Naqqas 3x miż-żewġ naħat.

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

L-ekwazzjoni hija f'forma standard.

$$3x^{2}a=y-3x$$

Iddividi ż-żewġ naħat b'3x^{2}.

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

Meta tiddividi b'3x^{2} titneħħa l-multiplikazzjoni b'3x^{2}.

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

Solvi għal a

$$\left\{\begin{matrix}a=\frac{y-3x}{3x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 3 b'ax^{2}+x.

$$y=3ax^{2}+3x$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$3ax^{2}+3x=y$$

Naqqas 3x miż-żewġ naħat.

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

L-ekwazzjoni hija f'forma standard.

$$3x^{2}a=y-3x$$

Iddividi ż-żewġ naħat b'3x^{2}.

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

Meta tiddividi b'3x^{2} titneħħa l-multiplikazzjoni b'3x^{2}.

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

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{3\left(4ay+3\right)}-3}{6a}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{4ay+3}+\sqrt{3}\right)}{6a}\text{, }&a\neq 0\\x=\frac{y}{3}\text{, }&a=0\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}x=\frac{\sqrt{3\left(4ay+3\right)}-3}{6a}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{4ay+3}+\sqrt{3}\right)}{6a}\text{, }&\left(y\leq -\frac{3}{4a}\text{ and }a<0\right)\text{ or }\left(y\geq -\frac{3}{4a}\text{ and }a>0\right)\text{ or }\left(a\neq 0\text{ and }y=-\frac{3}{4a}\right)\\x=\frac{y}{3}\text{, }&a=0\end{matrix}\right.$$