Solve 1422.1914-1.475x/sqrt{15}=x

$$1422.1914-1.475 \frac{ x }{ \sqrt{ 15 } } =x$$

Solve for x

$$x=-\frac{419546463\sqrt{15}}{2564875}+\frac{170662968}{102595}\approx 1029.944046334$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$1422.1914-1.475\times \frac{x\sqrt{15}}{\left(\sqrt{15}\right)^{2}}=x$$

The square of \sqrt{15} is 15.

$$1422.1914-1.475\times \frac{x\sqrt{15}}{15}=x$$

Subtract x from both sides.

$$1422.1914-1.475\times \frac{x\sqrt{15}}{15}-x=0$$

Multiply both sides of the equation by 15.

$$15\left(1422.1914-1.475\times \frac{x\sqrt{15}}{15}\right)-15x=0$$

Multiply both sides of the equation by 15.

$$225\left(1422.1914-1.475\times \frac{x\sqrt{15}}{15}\right)-225x=0$$

Use the distributive property to multiply 225 by 1422.1914-1.475\times \frac{x\sqrt{15}}{15}.

$$319993.065-331.875\times \frac{x\sqrt{15}}{15}-225x=0$$

Subtract 319993.065 from both sides. Anything subtracted from zero gives its negation.

$$-331.875\times \frac{x\sqrt{15}}{15}-225x=-319993.065$$

Multiply both sides of the equation by 15.

$$-331.875x\sqrt{15}-3375x=-4799895.975$$

Reorder the terms.

$$-331.875\sqrt{15}x-3375x=-4799895.975$$

Combine all terms containing x.

$$\left(-331.875\sqrt{15}-3375\right)x=-4799895.975$$

The equation is in standard form.

$$\left(-\frac{2655\sqrt{15}}{8}-3375\right)x=-4799895.975$$

Divide both sides by -331.875\sqrt{15}-3375.

$$\frac{\left(-\frac{2655\sqrt{15}}{8}-3375\right)x}{-\frac{2655\sqrt{15}}{8}-3375}=-\frac{4799895.975}{-\frac{2655\sqrt{15}}{8}-3375}$$

Dividing by -331.875\sqrt{15}-3375 undoes the multiplication by -331.875\sqrt{15}-3375.

$$x=-\frac{4799895.975}{-\frac{2655\sqrt{15}}{8}-3375}$$

Divide -4799895.975 by -331.875\sqrt{15}-3375.

$$x=-\frac{419546463\sqrt{15}}{2564875}+\frac{170662968}{102595}$$