Solve frac{2*5sqrt{7}}{2-5*7}=a*sqrt{7}

$$\frac { 2 \cdot 5 \sqrt { 7 } } { 2 - 5 \cdot 7 } = a \cdot \sqrt { 7 }$$

Solve for a

$$a=-\frac{10}{33}\approx -0.303030303$$

Steps for Solving Linear Equation

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{7}}{2-5\times 7}=a\sqrt{7}$$

Multiply 5 and 7 to get 35.

$$\frac{10\sqrt{7}}{2-35}=a\sqrt{7}$$

Subtract 35 from 2 to get -33.

$$\frac{10\sqrt{7}}{-33}=a\sqrt{7}$$

Swap sides so that all variable terms are on the left hand side.

$$a\sqrt{7}=\frac{10\sqrt{7}}{-33}$$

Multiply both sides of the equation by -33.

$$-33a\sqrt{7}=10\sqrt{7}$$

The equation is in standard form.

$$\left(-33\sqrt{7}\right)a=10\sqrt{7}$$

Divide both sides by -33\sqrt{7}.

$$\frac{\left(-33\sqrt{7}\right)a}{-33\sqrt{7}}=\frac{10\sqrt{7}}{-33\sqrt{7}}$$

Dividing by -33\sqrt{7} undoes the multiplication by -33\sqrt{7}.

$$a=\frac{10\sqrt{7}}{-33\sqrt{7}}$$

Divide 10\sqrt{7} by -33\sqrt{7}.

$$a=-\frac{10}{33}$$