Solve x^2/12+x/18-1/30

$$\frac { x ^ { 2 } } { 12 } + \frac { x } { 18 } - \frac { 1 } { 30 }$$

Evaluate

$$\frac{x^{2}}{12}+\frac{x}{18}-\frac{1}{30}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 18 is 36. Multiply \frac{x^{2}}{12} times \frac{3}{3}. Multiply \frac{x}{18} times \frac{2}{2}.

$$\frac{3x^{2}}{36}+\frac{2x}{36}-\frac{1}{30}$$

Since \frac{3x^{2}}{36} and \frac{2x}{36} have the same denominator, add them by adding their numerators.

$$\frac{3x^{2}+2x}{36}-\frac{1}{30}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 30 is 180. Multiply \frac{3x^{2}+2x}{36} times \frac{5}{5}. Multiply \frac{1}{30} times \frac{6}{6}.

$$\frac{5\left(3x^{2}+2x\right)}{180}-\frac{6}{180}$$

Since \frac{5\left(3x^{2}+2x\right)}{180} and \frac{6}{180} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(3x^{2}+2x\right)-6}{180}$$

Do the multiplications in 5\left(3x^{2}+2x\right)-6.

$$\frac{15x^{2}+10x-6}{180}$$

Factor

$$\frac{\left(x-\left(-\frac{\sqrt{115}}{15}-\frac{1}{3}\right)\right)\left(x-\left(\frac{\sqrt{115}}{15}-\frac{1}{3}\right)\right)}{12}$$