Solve 6.5=3x^2

$$6.5 = 3 { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{78}}{6} \approx 1.471960144$$

$$x = -\frac{\sqrt{78}}{6} \approx -1.471960144$$

Steps by Finding Square Root

Divide both sides by 3.

$$\frac{6.5}{3}=x^{2}$$

Expand \frac{6.5}{3} by multiplying both numerator and the denominator by 10.

$$\frac{65}{30}=x^{2}$$

Reduce the fraction \frac{65}{30} to lowest terms by extracting and canceling out 5.

$$\frac{13}{6}=x^{2}$$

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

$$x^{2}=\frac{13}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{78}}{6} x=-\frac{\sqrt{78}}{6}$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$\frac{6.5}{3}=x^{2}$$

Expand \frac{6.5}{3} by multiplying both numerator and the denominator by 10.

$$\frac{65}{30}=x^{2}$$

Reduce the fraction \frac{65}{30} to lowest terms by extracting and canceling out 5.

$$\frac{13}{6}=x^{2}$$

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

$$x^{2}=\frac{13}{6}$$

Subtract \frac{13}{6} from both sides.

$$x^{2}-\frac{13}{6}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{13}{6} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{13}{6}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{13}{6}\right)}}{2}$$

Multiply -4 times -\frac{13}{6}.

$$x=\frac{0±\sqrt{\frac{26}{3}}}{2}$$

Take the square root of \frac{26}{3}.

$$x=\frac{0±\frac{\sqrt{78}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{78}}{3}}{2} when ± is plus.

$$x=\frac{\sqrt{78}}{6}$$

Now solve the equation x=\frac{0±\frac{\sqrt{78}}{3}}{2} when ± is minus.

$$x=-\frac{\sqrt{78}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{78}}{6} x=-\frac{\sqrt{78}}{6}$$