Solve 5x^2-8x^2=3

$$5 { x }^{ 2 } -8 { x }^{ 2 } =3$$

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

Combine 5x^{2} and -8x^{2} to get -3x^{2}.

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

Divide both sides by -3.

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

Divide 3 by -3 to get -1.

$$x^{2}=-1$$

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

Combine 5x^{2} and -8x^{2} to get -3x^{2}.

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

Subtract 3 from both sides.

$$-3x^{2}-3=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-3\right)}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\left(-3\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\left(-3\right)}}{2\left(-3\right)}$$

Multiply 12 times -3.

$$x=\frac{0±\sqrt{-36}}{2\left(-3\right)}$$

Take the square root of -36.

$$x=\frac{0±6i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±6i}{-6}$$

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

$$x=-i$$

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

$$x=i$$

The equation is now solved.

$$x=-i x=i$$