Solve 5x^2+27=6

$$5 x ^ { 2 } + 27 = 6$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{105}i}{5}\approx -0-2.049390153i$$

$$x=\frac{\sqrt{105}i}{5}\approx 2.049390153i$$

Steps by Finding Square Root

Subtract 27 from both sides.

$$5x^{2}=6-27$$

Subtract 27 from 6 to get -21.

$$5x^{2}=-21$$

Divide both sides by 5.

$$x^{2}=-\frac{21}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{105}i}{5} x=-\frac{\sqrt{105}i}{5}$$

Steps Using the Quadratic Formula

Subtract 6 from both sides.

$$5x^{2}+27-6=0$$

Subtract 6 from 27 to get 21.

$$5x^{2}+21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 21}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 21}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 21}}{2\times 5}$$

Multiply -20 times 21.

$$x=\frac{0±\sqrt{-420}}{2\times 5}$$

Take the square root of -420.

$$x=\frac{0±2\sqrt{105}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{105}i}{10}$$

Now solve the equation x=\frac{0±2\sqrt{105}i}{10} when ± is plus.

$$x=\frac{\sqrt{105}i}{5}$$

Now solve the equation x=\frac{0±2\sqrt{105}i}{10} when ± is minus.

$$x=-\frac{\sqrt{105}i}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{105}i}{5} x=-\frac{\sqrt{105}i}{5}$$