Solve x+13=2*x^2+25/2x

$$x + 13 = 2 \cdot \frac { x ^ { 2 } + 25 } { 2 x }$$

Solve for x

$$x = \frac{25}{13} = 1\frac{12}{13} \approx 1.923076923$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x.

$$2xx+2x\times 13=2\left(x^{2}+25\right)$$

Multiply x and x to get x^{2}.

$$2x^{2}+2x\times 13=2\left(x^{2}+25\right)$$

Multiply 2 and 13 to get 26.

$$2x^{2}+26x=2\left(x^{2}+25\right)$$

Use the distributive property to multiply 2 by x^{2}+25.

$$2x^{2}+26x=2x^{2}+50$$

Subtract 2x^{2} from both sides.

$$2x^{2}+26x-2x^{2}=50$$

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

$$26x=50$$

Divide both sides by 26.

$$x=\frac{50}{26}$$

Reduce the fraction \frac{50}{26} to lowest terms by extracting and canceling out 2.

$$x=\frac{25}{13}$$