Solve 3x^2+45=8

$$3 { x }^{ 2 } +45=8$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{111}i}{3}\approx -0-3.511884584i$$

$$x=\frac{\sqrt{111}i}{3}\approx 3.511884584i$$

Steps by Finding Square Root

Subtract 45 from both sides.

$$3x^{2}=8-45$$

Subtract 45 from 8 to get -37.

$$3x^{2}=-37$$

Divide both sides by 3.

$$x^{2}=-\frac{37}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{111}i}{3} x=-\frac{\sqrt{111}i}{3}$$

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$3x^{2}+45-8=0$$

Subtract 8 from 45 to get 37.

$$3x^{2}+37=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 37 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 37}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 37}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 37}}{2\times 3}$$

Multiply -12 times 37.

$$x=\frac{0±\sqrt{-444}}{2\times 3}$$

Take the square root of -444.

$$x=\frac{0±2\sqrt{111}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{111}i}{6}$$

Now solve the equation x=\frac{0±2\sqrt{111}i}{6} when ± is plus.

$$x=\frac{\sqrt{111}i}{3}$$

Now solve the equation x=\frac{0±2\sqrt{111}i}{6} when ± is minus.

$$x=-\frac{\sqrt{111}i}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{111}i}{3} x=-\frac{\sqrt{111}i}{3}$$