Solve Dx=(3x^2+17/20x-10)

$$D x = ( \frac { 3 x ^ { 2 } + 17 } { 20 x - 10 } )$$

Solve for D

$$D=\frac{3x^{2}+17}{10x\left(2x-1\right)}$$

$$x\neq \frac{1}{2}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10\left(2x-1\right).

$$Dx\times 10\left(2x-1\right)=3x^{2}+17$$

Use the distributive property to multiply Dx\times 10 by 2x-1.

$$20Dx^{2}-Dx\times 10=3x^{2}+17$$

Multiply -1 and 10 to get -10.

$$20Dx^{2}-10Dx=3x^{2}+17$$

Combine all terms containing D.

$$\left(20x^{2}-10x\right)D=3x^{2}+17$$

Divide both sides by 20x^{2}-10x.

$$\frac{\left(20x^{2}-10x\right)D}{20x^{2}-10x}=\frac{3x^{2}+17}{20x^{2}-10x}$$

Dividing by 20x^{2}-10x undoes the multiplication by 20x^{2}-10x.

$$D=\frac{3x^{2}+17}{20x^{2}-10x}$$

Divide 3x^{2}+17 by 20x^{2}-10x.

$$D=\frac{3x^{2}+17}{10x\left(2x-1\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{25D^{2}+340D-51}+5D}{20D-3}\text{; }x=\frac{-\sqrt{25D^{2}+340D-51}+5D}{20D-3}\text{, }&D\neq \frac{3}{20}\\x=-\frac{34}{3}\text{, }&D=\frac{3}{20}\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{25D^{2}+340D-51}+5D}{20D-3}\text{; }x=\frac{-\sqrt{25D^{2}+340D-51}+5D}{20D-3}\text{, }&D\leq \frac{-\sqrt{1207}-34}{5}\text{ or }\left(D\neq \frac{3}{20}\text{ and }D\geq \frac{\sqrt{1207}-34}{5}\right)\\x=-\frac{34}{3}\text{, }&D=\frac{3}{20}\end{matrix}\right.$$