Solve n6x^2+11x-10=0

$$n 6 x ^ { 2 } + 11 x - 10 = 0$$

Solve for n_6

$$n_{6}=-\frac{11x-10}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 11x from both sides. Anything subtracted from zero gives its negation.

$$n_{6}x^{2}-10=-11x$$

Add 10 to both sides.

$$n_{6}x^{2}=-11x+10$$

The equation is in standard form.

$$x^{2}n_{6}=10-11x$$

Divide both sides by x^{2}.

$$\frac{x^{2}n_{6}}{x^{2}}=\frac{10-11x}{x^{2}}$$

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

$$n_{6}=\frac{10-11x}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{40n_{6}+121}-11}{2n_{6}}\text{; }x=-\frac{\sqrt{40n_{6}+121}+11}{2n_{6}}\text{, }&n_{6}\neq 0\\x=\frac{10}{11}\text{, }&n_{6}=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{40n_{6}+121}-11}{2n_{6}}\text{; }x=-\frac{\sqrt{40n_{6}+121}+11}{2n_{6}}\text{, }&n_{6}\neq 0\text{ and }n_{6}\geq -\frac{121}{40}\\x=\frac{10}{11}\text{, }&n_{6}=0\end{matrix}\right.$$