Solve 6x^2-4=-43

$$6 x ^ { 2 } - 4 = - 43$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{26}i}{2}\approx -0-2.549509757i$$

$$x=\frac{\sqrt{26}i}{2}\approx 2.549509757i$$

Steps by Finding Square Root

Add 4 to both sides.

$$6x^{2}=-43+4$$

Add -43 and 4 to get -39.

$$6x^{2}=-39$$

Divide both sides by 6.

$$x^{2}=\frac{-39}{6}$$

Reduce the fraction \frac{-39}{6} to lowest terms by extracting and canceling out 3.

$$x^{2}=-\frac{13}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{26}i}{2} x=-\frac{\sqrt{26}i}{2}$$

Steps Using the Quadratic Formula

Add 43 to both sides.

$$6x^{2}-4+43=0$$

Add -4 and 43 to get 39.

$$6x^{2}+39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 39}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 39}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 39}}{2\times 6}$$

Multiply -24 times 39.

$$x=\frac{0±\sqrt{-936}}{2\times 6}$$

Take the square root of -936.

$$x=\frac{0±6\sqrt{26}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±6\sqrt{26}i}{12}$$

Now solve the equation x=\frac{0±6\sqrt{26}i}{12} when ± is plus.

$$x=\frac{\sqrt{26}i}{2}$$

Now solve the equation x=\frac{0±6\sqrt{26}i}{12} when ± is minus.

$$x=-\frac{\sqrt{26}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{26}i}{2} x=-\frac{\sqrt{26}i}{2}$$