Solve left(350+5/8xright)*x=150+5*(80-x)/8*(80-x)

$$\left( 350+ \frac{ 5 }{ 8 } x \right) \times x = 150+ \frac{ 5 \times (80-x) }{ 8 } \times (80-x)$$

Solve for x

$$x = \frac{83}{9} = 9\frac{2}{9} \approx 9.222222222$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8.

$$8\left(350+\frac{5}{8}x\right)x=1200+5\left(80-x\right)\left(80-x\right)$$

Use the distributive property to multiply 8 by 350+\frac{5}{8}x.

$$\left(2800+8\times \frac{5}{8}x\right)x=1200+5\left(80-x\right)\left(80-x\right)$$

Cancel out 8 and 8.

$$\left(2800+5x\right)x=1200+5\left(80-x\right)\left(80-x\right)$$

Use the distributive property to multiply 2800+5x by x.

$$2800x+5x^{2}=1200+5\left(80-x\right)\left(80-x\right)$$

Multiply 80-x and 80-x to get \left(80-x\right)^{2}.

$$2800x+5x^{2}=1200+5\left(80-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(80-x\right)^{2}.

$$2800x+5x^{2}=1200+5\left(6400-160x+x^{2}\right)$$

Use the distributive property to multiply 5 by 6400-160x+x^{2}.

$$2800x+5x^{2}=1200+32000-800x+5x^{2}$$

Add 1200 and 32000 to get 33200.

$$2800x+5x^{2}=33200-800x+5x^{2}$$

Add 800x to both sides.

$$2800x+5x^{2}+800x=33200+5x^{2}$$

Combine 2800x and 800x to get 3600x.

$$3600x+5x^{2}=33200+5x^{2}$$

Subtract 5x^{2} from both sides.

$$3600x+5x^{2}-5x^{2}=33200$$

Combine 5x^{2} and -5x^{2} to get 0.

$$3600x=33200$$

Divide both sides by 3600.

$$x=\frac{33200}{3600}$$

Reduce the fraction \frac{33200}{3600} to lowest terms by extracting and canceling out 400.

$$x=\frac{83}{9}$$