Solve x+9^65=5^6b/x

$$x + 9 ^ { 6 } 5 = \frac { 5 ^ { 6 } b } { x }$$

Solve for b

$$b=\frac{x\left(x+2657205\right)}{15625}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$xx+9^{6}\times 5x=5^{6}b$$

Multiply x and x to get x^{2}.

$$x^{2}+9^{6}\times 5x=5^{6}b$$

Calculate 9 to the power of 6 and get 531441.

$$x^{2}+531441\times 5x=5^{6}b$$

Multiply 531441 and 5 to get 2657205.

$$x^{2}+2657205x=5^{6}b$$

Calculate 5 to the power of 6 and get 15625.

$$x^{2}+2657205x=15625b$$

Swap sides so that all variable terms are on the left hand side.

$$15625b=x^{2}+2657205x$$

Divide both sides by 15625.

$$\frac{15625b}{15625}=\frac{x\left(x+2657205\right)}{15625}$$

Dividing by 15625 undoes the multiplication by 15625.

$$b=\frac{x\left(x+2657205\right)}{15625}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{-5\sqrt{2500b+282429536481}-2657205}{2}\text{, }&\text{unconditionally}\\x=\frac{5\sqrt{2500b+282429536481}-2657205}{2}\text{, }&b\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-5\sqrt{2500b+282429536481}-2657205}{2}\text{, }&b\geq -\frac{282429536481}{2500}\\x=\frac{5\sqrt{2500b+282429536481}-2657205}{2}\text{, }&b\neq 0\text{ and }b\geq -\frac{282429536481}{2500}\end{matrix}\right.$$