Solve 3(x-5/6)^2=49/12

$$3 ( x - \frac { 5 } { 6 } ) ^ { 2 } = \frac { 49 } { 12 }$$

Solve for x

$$x=2$$

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps by Finding Square Root

Divide both sides by 3.

$$\frac{3\left(x-\frac{5}{6}\right)^{2}}{3}=\frac{\frac{49}{12}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x-\frac{5}{6}\right)^{2}=\frac{\frac{49}{12}}{3}$$

Divide \frac{49}{12} by 3.

$$\left(x-\frac{5}{6}\right)^{2}=\frac{49}{36}$$

Take the square root of both sides of the equation.

$$x-\frac{5}{6}=\frac{7}{6} x-\frac{5}{6}=-\frac{7}{6}$$

Add \frac{5}{6} to both sides of the equation.

$$x-\frac{5}{6}-\left(-\frac{5}{6}\right)=\frac{7}{6}-\left(-\frac{5}{6}\right) x-\frac{5}{6}-\left(-\frac{5}{6}\right)=-\frac{7}{6}-\left(-\frac{5}{6}\right)$$

Subtracting -\frac{5}{6} from itself leaves 0.

$$x=\frac{7}{6}-\left(-\frac{5}{6}\right) x=-\frac{7}{6}-\left(-\frac{5}{6}\right)$$

Subtract -\frac{5}{6} from \frac{7}{6} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=2$$

Subtract -\frac{5}{6} from -\frac{7}{6} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{1}{3}$$

The equation is now solved.

$$x=2 x=-\frac{1}{3}$$