Issolvi y=ax^2-(2a-3)x+(a-1)

$$y = a x ^ { 2 } - ( 2 a - 3 ) x + ( a - 1 )$$

Solvi għal a (complex solution)

$$\left\{\begin{matrix}a=-\frac{3x-y-1}{\left(x-1\right)^{2}}\text{, }&x\neq 1\\a\in \mathrm{C}\text{, }&y=2\text{ and }x=1\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 2a-3 b'x.

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

Biex issib l-oppost ta' 2ax-3x, sib l-oppost ta' kull terminu.

$$y=ax^{2}-2ax+3x+a-1$$

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

$$ax^{2}-2ax+3x+a-1=y$$

Naqqas 3x miż-żewġ naħat.

$$ax^{2}-2ax+a-1=y-3x$$

Żid 1 maż-żewġ naħat.

$$ax^{2}-2ax+a=y-3x+1$$

Ikkombina t-termini kollha li fihom a.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'x^{2}-2x+1.

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

Meta tiddividi b'x^{2}-2x+1 titneħħa l-multiplikazzjoni b'x^{2}-2x+1.

$$a=\frac{1+y-3x}{x^{2}-2x+1}$$

Iddividi y-3x+1 b'x^{2}-2x+1.

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

Solvi għal a

$$\left\{\begin{matrix}a=-\frac{3x-y-1}{\left(x-1\right)^{2}}\text{, }&x\neq 1\\a\in \mathrm{R}\text{, }&y=2\text{ and }x=1\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 2a-3 b'x.

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

Biex issib l-oppost ta' 2ax-3x, sib l-oppost ta' kull terminu.

$$y=ax^{2}-2ax+3x+a-1$$

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

$$ax^{2}-2ax+3x+a-1=y$$

Naqqas 3x miż-żewġ naħat.

$$ax^{2}-2ax+a-1=y-3x$$

Żid 1 maż-żewġ naħat.

$$ax^{2}-2ax+a=y-3x+1$$

Ikkombina t-termini kollha li fihom a.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'x^{2}-2x+1.

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

Meta tiddividi b'x^{2}-2x+1 titneħħa l-multiplikazzjoni b'x^{2}-2x+1.

$$a=\frac{1+y-3x}{x^{2}-2x+1}$$

Iddividi y-3x+1 b'x^{2}-2x+1.

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

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4ay-8a+9}+2a-3}{2a}\text{; }x=\frac{-\sqrt{4ay-8a+9}+2a-3}{2a}\text{, }&a\neq 0\\x=\frac{y+1}{3}\text{, }&a=0\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}x=\frac{\sqrt{4ay-8a+9}+2a-3}{2a}\text{; }x=\frac{-\sqrt{4ay-8a+9}+2a-3}{2a}\text{, }&\left(a>0\text{ or }y\leq 2-\frac{9}{4a}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }a\neq 0\right)\text{ and }\left(a<0\text{ or }\left(a\neq 0\text{ and }y\geq 2-\frac{9}{4a}\right)\right)\\x=\frac{y+1}{3}\text{, }&a=0\end{matrix}\right.$$