Solve 5x/8+5^3=z*x^2

$$\frac{ 5x }{ 8 } + { 5 }^{ 3 } =z \times { x }^{ 2 }$$

Solve for z

$$z=\frac{5\left(x+200\right)}{8x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8.

$$5x+8\times 5^{3}=8zx^{2}$$

Calculate 5 to the power of 3 and get 125.

$$5x+8\times 125=8zx^{2}$$

Multiply 8 and 125 to get 1000.

$$5x+1000=8zx^{2}$$

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

$$8zx^{2}=5x+1000$$

The equation is in standard form.

$$8x^{2}z=5x+1000$$

Divide both sides by 8x^{2}.

$$\frac{8x^{2}z}{8x^{2}}=\frac{5x+1000}{8x^{2}}$$

Dividing by 8x^{2} undoes the multiplication by 8x^{2}.

$$z=\frac{5x+1000}{8x^{2}}$$

Divide 1000+5x by 8x^{2}.

$$z=\frac{5\left(x+200\right)}{8x^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{5\left(\sqrt{1280z+1}-1\right)}{16z}\text{; }x=\frac{5\left(\sqrt{1280z+1}+1\right)}{16z}\text{, }&z\neq 0\text{ and }z\geq -\frac{1}{1280}\\x=-200\text{, }&z=0\end{matrix}\right.$$