Solve 3x^2+19+1=0

$$3 { x }^{ 2 } +19+1=0$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{15}i}{3}\approx -0-2.581988897i$$

$$x=\frac{2\sqrt{15}i}{3}\approx 2.581988897i$$

Steps by Finding Square Root

Add 19 and 1 to get 20.

$$3x^{2}+20=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$3x^{2}=-20$$

Divide both sides by 3.

$$x^{2}=-\frac{20}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}i}{3} x=-\frac{2\sqrt{15}i}{3}$$

Steps Using the Quadratic Formula

Add 19 and 1 to get 20.

$$3x^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 20}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 20}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 20}}{2\times 3}$$

Multiply -12 times 20.

$$x=\frac{0±\sqrt{-240}}{2\times 3}$$

Take the square root of -240.

$$x=\frac{0±4\sqrt{15}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±4\sqrt{15}i}{6}$$

Now solve the equation x=\frac{0±4\sqrt{15}i}{6} when ± is plus.

$$x=\frac{2\sqrt{15}i}{3}$$

Now solve the equation x=\frac{0±4\sqrt{15}i}{6} when ± is minus.

$$x=-\frac{2\sqrt{15}i}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}i}{3} x=-\frac{2\sqrt{15}i}{3}$$