Solve frac{-7-sqrt{7^2-4*6*2}}{2*6}

$$\frac{ -7- \sqrt{ { 7 }^{ 2 } -4 \times 6 \times 2 } }{ 2 \times 6 }$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$\frac{-7-\sqrt{49-4\times 6\times 2}}{2\times 6}$$

Multiply 4 and 6 to get 24.

$$\frac{-7-\sqrt{49-24\times 2}}{2\times 6}$$

Multiply 24 and 2 to get 48.

$$\frac{-7-\sqrt{49-48}}{2\times 6}$$

Subtract 48 from 49 to get 1.

$$\frac{-7-\sqrt{1}}{2\times 6}$$

Calculate the square root of 1 and get 1.

$$\frac{-7-1}{2\times 6}$$

Subtract 1 from -7 to get -8.

$$\frac{-8}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{-8}{12}$$

Reduce the fraction \frac{-8}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{2}{3}$$

Factor

$$-\frac{2}{3} = -0.6666666666666666$$