Solve kx^2+5x/4=5

$$\frac { k x ^ { 2 } + 5 x } { 4 } = 5$$

Solve for k

$$k=-\frac{5\left(x-4\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides by 4.

$$kx^{2}+5x=5\times 4$$

Multiply 5 and 4 to get 20.

$$kx^{2}+5x=20$$

Subtract 5x from both sides.

$$kx^{2}=20-5x$$

The equation is in standard form.

$$x^{2}k=20-5x$$

Divide both sides by x^{2}.

$$\frac{x^{2}k}{x^{2}}=\frac{20-5x}{x^{2}}$$

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

$$k=\frac{20-5x}{x^{2}}$$

Divide 20-5x by x^{2}.

$$k=\frac{5\left(4-x\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{5\left(16k+5\right)}-5}{2k}\text{; }x=-\frac{\sqrt{5}\left(\sqrt{16k+5}+\sqrt{5}\right)}{2k}\text{, }&k\neq 0\\x=4\text{, }&k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{5\left(16k+5\right)}-5}{2k}\text{; }x=-\frac{\sqrt{5}\left(\sqrt{16k+5}+\sqrt{5}\right)}{2k}\text{, }&k\neq 0\text{ and }k\geq -\frac{5}{16}\\x=4\text{, }&k=0\end{matrix}\right.$$