Solve 3x^2-5=4

$$3 { x }^{ 2 } -5=4$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Add 5 to both sides.

$$3x^{2}=4+5$$

Add 4 and 5 to get 9.

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

Divide both sides by 3.

$$x^{2}=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

$$x=\sqrt{3} x=-\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$3x^{2}-5-4=0$$

Subtract 4 from -5 to get -9.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-9\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-9\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-9\right)}}{2\times 3}$$

Multiply -12 times -9.

$$x=\frac{0±\sqrt{108}}{2\times 3}$$

Take the square root of 108.

$$x=\frac{0±6\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±6\sqrt{3}}{6} when ± is plus.

$$x=\sqrt{3}$$

Now solve the equation x=\frac{0±6\sqrt{3}}{6} when ± is minus.

$$x=-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3} x=-\sqrt{3}$$