Solve 20x+x3/3+29/3=120x+15x^2/2+45/2

$$20x+ \frac{ x3 }{ 3 } + \frac{ 29 }{ 3 } =120x+ \frac{ 15 { x }^{ 2 } }{ 2 } + \frac{ 45 }{ 2 }$$

Solve for x_3

$$x_{3}=\frac{45x^{2}}{2}+300x+\frac{77}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$120x+2x_{3}+58=720x+3\times 15x^{2}+135$$

Multiply 3 and 15 to get 45.

$$120x+2x_{3}+58=720x+45x^{2}+135$$

Subtract 120x from both sides.

$$2x_{3}+58=720x+45x^{2}+135-120x$$

Combine 720x and -120x to get 600x.

$$2x_{3}+58=600x+45x^{2}+135$$

Subtract 58 from both sides.

$$2x_{3}=600x+45x^{2}+135-58$$

Subtract 58 from 135 to get 77.

$$2x_{3}=600x+45x^{2}+77$$

The equation is in standard form.

$$2x_{3}=45x^{2}+600x+77$$

Divide both sides by 2.

$$\frac{2x_{3}}{2}=\frac{45x^{2}+600x+77}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x_{3}=\frac{45x^{2}+600x+77}{2}$$

Divide 600x+45x^{2}+77 by 2.

$$x_{3}=\frac{45x^{2}}{2}+300x+\frac{77}{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{10x_{3}+9615}}{15}-\frac{20}{3}$$

$$x=\frac{\sqrt{10x_{3}+9615}}{15}-\frac{20}{3}$$

Solve for x

$$x=-\frac{\sqrt{10x_{3}+9615}}{15}-\frac{20}{3}$$

$$x=\frac{\sqrt{10x_{3}+9615}}{15}-\frac{20}{3}\text{, }x_{3}\geq -\frac{1923}{2}$$