Solve 5x^2+6=2

$$5 x ^ { 2 } + 6 = 2$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{5}i}{5}\approx -0-0.894427191i$$

$$x=\frac{2\sqrt{5}i}{5}\approx 0.894427191i$$

Steps by Finding Square Root

Subtract 6 from both sides.

$$5x^{2}=2-6$$

Subtract 6 from 2 to get -4.

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

Divide both sides by 5.

$$x^{2}=-\frac{4}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{5}i}{5} x=-\frac{2\sqrt{5}i}{5}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$5x^{2}+6-2=0$$

Subtract 2 from 6 to get 4.

$$5x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 4}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 4}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 4}}{2\times 5}$$

Multiply -20 times 4.

$$x=\frac{0±\sqrt{-80}}{2\times 5}$$

Take the square root of -80.

$$x=\frac{0±4\sqrt{5}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±4\sqrt{5}i}{10}$$

Now solve the equation x=\frac{0±4\sqrt{5}i}{10} when ± is plus.

$$x=\frac{2\sqrt{5}i}{5}$$

Now solve the equation x=\frac{0±4\sqrt{5}i}{10} when ± is minus.

$$x=-\frac{2\sqrt{5}i}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{5}i}{5} x=-\frac{2\sqrt{5}i}{5}$$