Solve operatorname{la}34x^2-x=39

$$\operatorname { la } 34 x ^ { 2 } - x = 39$$

Solve for a_34 (complex solution)

$$\left\{\begin{matrix}a_{34}=\frac{x+39}{lx^{2}}\text{, }&x\neq 0\text{ and }l\neq 0\\a_{34}\in \mathrm{C}\text{, }&x=-39\text{ and }l=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides.

$$la_{34}x^{2}=39+x$$

The equation is in standard form.

$$lx^{2}a_{34}=x+39$$

Divide both sides by lx^{2}.

$$\frac{lx^{2}a_{34}}{lx^{2}}=\frac{x+39}{lx^{2}}$$

Dividing by lx^{2} undoes the multiplication by lx^{2}.

$$a_{34}=\frac{x+39}{lx^{2}}$$

Solve for l (complex solution)

$$\left\{\begin{matrix}l=\frac{x+39}{a_{34}x^{2}}\text{, }&x\neq 0\text{ and }a_{34}\neq 0\\l\in \mathrm{C}\text{, }&x=-39\text{ and }a_{34}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides.

$$la_{34}x^{2}=39+x$$

The equation is in standard form.

$$a_{34}x^{2}l=x+39$$

Divide both sides by a_{34}x^{2}.

$$\frac{a_{34}x^{2}l}{a_{34}x^{2}}=\frac{x+39}{a_{34}x^{2}}$$

Dividing by a_{34}x^{2} undoes the multiplication by a_{34}x^{2}.

$$l=\frac{x+39}{a_{34}x^{2}}$$

Solve for a_34

$$\left\{\begin{matrix}a_{34}=\frac{x+39}{lx^{2}}\text{, }&x\neq 0\text{ and }l\neq 0\\a_{34}\in \mathrm{R}\text{, }&x=-39\text{ and }l=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides.

$$la_{34}x^{2}=39+x$$

The equation is in standard form.

$$lx^{2}a_{34}=x+39$$

Divide both sides by lx^{2}.

$$\frac{lx^{2}a_{34}}{lx^{2}}=\frac{x+39}{lx^{2}}$$

Dividing by lx^{2} undoes the multiplication by lx^{2}.

$$a_{34}=\frac{x+39}{lx^{2}}$$

Solve for l

$$\left\{\begin{matrix}l=\frac{x+39}{a_{34}x^{2}}\text{, }&x\neq 0\text{ and }a_{34}\neq 0\\l\in \mathrm{R}\text{, }&x=-39\text{ and }a_{34}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides.

$$la_{34}x^{2}=39+x$$

The equation is in standard form.

$$a_{34}x^{2}l=x+39$$

Divide both sides by a_{34}x^{2}.

$$\frac{a_{34}x^{2}l}{a_{34}x^{2}}=\frac{x+39}{a_{34}x^{2}}$$

Dividing by a_{34}x^{2} undoes the multiplication by a_{34}x^{2}.

$$l=\frac{x+39}{a_{34}x^{2}}$$