Solve 3x^2+9=51

$$3 x ^ { 2 } + 9 = 51$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Subtract 9 from both sides.

$$3x^{2}=51-9$$

Subtract 9 from 51 to get 42.

$$3x^{2}=42$$

Divide both sides by 3.

$$x^{2}=\frac{42}{3}$$

Divide 42 by 3 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

$$x=\sqrt{14} x=-\sqrt{14}$$

Steps Using the Quadratic Formula

Subtract 51 from both sides.

$$3x^{2}+9-51=0$$

Subtract 51 from 9 to get -42.

$$3x^{2}-42=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-42\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-42\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-42\right)}}{2\times 3}$$

Multiply -12 times -42.

$$x=\frac{0±\sqrt{504}}{2\times 3}$$

Take the square root of 504.

$$x=\frac{0±6\sqrt{14}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{14}}{6}$$

Now solve the equation x=\frac{0±6\sqrt{14}}{6} when ± is plus.

$$x=\sqrt{14}$$

Now solve the equation x=\frac{0±6\sqrt{14}}{6} when ± is minus.

$$x=-\sqrt{14}$$

The equation is now solved.

$$x=\sqrt{14} x=-\sqrt{14}$$