Issolvi 2an+n(n-1)/2x(-3)=70

$$2 a n + \frac { n ( n - 1 ) } { 2 } x ( - 3 ) = 70$$

Solvi għal a

$$a=\frac{3nx}{4}-\frac{3x}{4}+\frac{35}{n}$$

$$n\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2.

$$4an+n\left(n-1\right)x\left(-3\right)=140$$

Uża l-propjetà distributtiva biex timmultiplika n b'n-1.

$$4an+\left(n^{2}-n\right)x\left(-3\right)=140$$

Uża l-propjetà distributtiva biex timmultiplika n^{2}-n b'x.

$$4an+\left(n^{2}x-nx\right)\left(-3\right)=140$$

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

$$4an-3n^{2}x+3nx=140$$

Żid 3n^{2}x maż-żewġ naħat.

$$4an+3nx=140+3n^{2}x$$

Naqqas 3nx miż-żewġ naħat.

$$4an=140+3n^{2}x-3nx$$

L-ekwazzjoni hija f'forma standard.

$$4na=3xn^{2}-3nx+140$$

Iddividi ż-żewġ naħat b'4n.

$$\frac{4na}{4n}=\frac{3xn^{2}-3nx+140}{4n}$$

Meta tiddividi b'4n titneħħa l-multiplikazzjoni b'4n.

$$a=\frac{3xn^{2}-3nx+140}{4n}$$

Iddividi 140+3n^{2}x-3nx b'4n.

$$a=\frac{3nx}{4}-\frac{3x}{4}+\frac{35}{n}$$

Solvi għal n (complex solution)

$$\left\{\begin{matrix}n=-\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}-3x-4a}{6x}\text{; }n=\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}+3x+4a}{6x}\text{, }&x\neq 0\\n=\frac{35}{a}\text{, }&x=0\text{ and }a\neq 0\end{matrix}\right.$$

Solvi għal n

$$\left\{\begin{matrix}n=-\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}-3x-4a}{6x}\text{; }n=\frac{\sqrt{9x^{2}+24ax-1680x+16a^{2}}+3x+4a}{6x}\text{, }&\left(x\neq 0\text{ and }a\geq -\frac{3x}{4}+\sqrt{105x}\right)\text{ or }\left(x\neq 0\text{ and }a\leq -\frac{3x}{4}-\sqrt{105x}\right)\text{ or }x<0\\n=\frac{35}{a}\text{, }&x=0\text{ and }a\neq 0\end{matrix}\right.$$