Solve (30-sqrt{3}x)tan(15)=x

$$(30- \sqrt{ 3 } x) \tan ( 15 ) =x$$

Solve for x

$$x = \frac{803847577293368100000000000000000 - 215390309173472467264750747365870 \sqrt{3}}{78460969082652753273524925263413} = 5\frac{3.847577293368118 \times 10^{31}}{7.846096908265276 \times 10^{31}} \approx 5.490381057$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$${(30 - \sqrt{3} x)} 0.2679491924311227 = x$$

Subtract x from both sides.

$$0.2679491924311227\left(30-\sqrt{3}x\right)-x=0$$

Use the distributive property to multiply 0.2679491924311227 by 30-\sqrt{3}x.

$$8.038475772933681-0.2679491924311227\sqrt{3}x-x=0$$

Subtract 8.038475772933681 from both sides. Anything subtracted from zero gives its negation.

$$-0.2679491924311227\sqrt{3}x-x=-8.038475772933681$$

Combine all terms containing x.

$$\left(-0.2679491924311227\sqrt{3}-1\right)x=-8.038475772933681$$

The equation is in standard form.

$$\left(-\frac{2679491924311227\sqrt{3}}{10000000000000000}-1\right)x=-8.038475772933681$$

Divide both sides by -0.2679491924311227\sqrt{3}-1.

$$\frac{\left(-\frac{2679491924311227\sqrt{3}}{10000000000000000}-1\right)x}{-\frac{2679491924311227\sqrt{3}}{10000000000000000}-1}=-\frac{8.038475772933681}{-\frac{2679491924311227\sqrt{3}}{10000000000000000}-1}$$

Dividing by -0.2679491924311227\sqrt{3}-1 undoes the multiplication by -0.2679491924311227\sqrt{3}-1.

$$x=-\frac{8.038475772933681}{-\frac{2679491924311227\sqrt{3}}{10000000000000000}-1}$$

Divide -8.038475772933681 by -0.2679491924311227\sqrt{3}-1.

$$x=\frac{803847577293368100000000000000000-215390309173472467264750747365870\sqrt{3}}{78460969082652753273524925263413}$$