Solve 7x^2/4-6x/7-1/7

$$\frac { 7 x ^ { 2 } } { 4 } - \frac { 6 x } { 7 } - \frac { 1 } { 7 }$$

Evaluate

$$\frac{7x^{2}}{4}-\frac{6x}{7}-\frac{1}{7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 7 is 28. Multiply \frac{7x^{2}}{4} times \frac{7}{7}. Multiply \frac{6x}{7} times \frac{4}{4}.

$$\frac{7\times 7x^{2}}{28}-\frac{4\times 6x}{28}-\frac{1}{7}$$

Since \frac{7\times 7x^{2}}{28} and \frac{4\times 6x}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\times 7x^{2}-4\times 6x}{28}-\frac{1}{7}$$

Do the multiplications in 7\times 7x^{2}-4\times 6x.

$$\frac{49x^{2}-24x}{28}-\frac{1}{7}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 28 and 7 is 28. Multiply \frac{1}{7} times \frac{4}{4}.

$$\frac{49x^{2}-24x}{28}-\frac{4}{28}$$

Since \frac{49x^{2}-24x}{28} and \frac{4}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49x^{2}-24x-4}{28}$$

Factor

$$\frac{7\left(x-\frac{12-2\sqrt{85}}{49}\right)\left(x-\frac{2\sqrt{85}+12}{49}\right)}{4}$$