Solve 3x^2+2/3=10

$$\frac { 3 x ^ { 2 } + 2 } { 3 } = 10$$

Solve for x

$$x = \frac{2 \sqrt{21}}{3} \approx 3.055050463$$

$$x = -\frac{2 \sqrt{21}}{3} \approx -3.055050463$$

Steps by Finding Square Root

Multiply both sides by 3.

$$3x^{2}+2=10\times 3$$

Multiply 10 and 3 to get 30.

$$3x^{2}+2=30$$

Subtract 2 from both sides.

$$3x^{2}=30-2$$

Subtract 2 from 30 to get 28.

$$3x^{2}=28$$

Divide both sides by 3.

$$x^{2}=\frac{28}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{21}}{3} x=-\frac{2\sqrt{21}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides by 3.

$$3x^{2}+2=10\times 3$$

Multiply 10 and 3 to get 30.

$$3x^{2}+2=30$$

Subtract 30 from both sides.

$$3x^{2}+2-30=0$$

Subtract 30 from 2 to get -28.

$$3x^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-28\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-28\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-28\right)}}{2\times 3}$$

Multiply -12 times -28.

$$x=\frac{0±\sqrt{336}}{2\times 3}$$

Take the square root of 336.

$$x=\frac{0±4\sqrt{21}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±4\sqrt{21}}{6}$$

Now solve the equation x=\frac{0±4\sqrt{21}}{6} when ± is plus.

$$x=\frac{2\sqrt{21}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{21}}{6} when ± is minus.

$$x=-\frac{2\sqrt{21}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{21}}{3} x=-\frac{2\sqrt{21}}{3}$$