Solve 12/5+57/1x-sqrt{57}=3

$$\frac{ 12 }{ 5 } + \frac{ 57 }{ 1x } - \sqrt{ 57 } = 3$$

Solve for x

$$x = \frac{475 \sqrt{57} - 285}{472} \approx 6.994007112$$

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 5x, the least common multiple of 5,1x.

$$5x\times \frac{12}{5}+5\times 57-\sqrt{57}\times 5x=15x$$

Multiply 5 and \frac{12}{5} to get 12.

$$12x+5\times 57-\sqrt{57}\times 5x=15x$$

Multiply 5 and 57 to get 285.

$$12x+285-\sqrt{57}\times 5x=15x$$

Multiply -1 and 5 to get -5.

$$12x+285-5\sqrt{57}x=15x$$

Subtract 15x from both sides.

$$12x+285-5\sqrt{57}x-15x=0$$

Combine 12x and -15x to get -3x.

$$-3x+285-5\sqrt{57}x=0$$

Subtract 285 from both sides. Anything subtracted from zero gives its negation.

$$-3x-5\sqrt{57}x=-285$$

Combine all terms containing x.

$$\left(-3-5\sqrt{57}\right)x=-285$$

The equation is in standard form.

$$\left(-5\sqrt{57}-3\right)x=-285$$

Divide both sides by -3-5\sqrt{57}.

$$\frac{\left(-5\sqrt{57}-3\right)x}{-5\sqrt{57}-3}=-\frac{285}{-5\sqrt{57}-3}$$

Dividing by -3-5\sqrt{57} undoes the multiplication by -3-5\sqrt{57}.

$$x=-\frac{285}{-5\sqrt{57}-3}$$

Divide -285 by -3-5\sqrt{57}.

$$x=\frac{475\sqrt{57}-285}{472}$$