Solve 15x^2+8=0

$$15 { x }^{ 2 } +8=0$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{30}i}{15}\approx -0-0.730296743i$$

$$x=\frac{2\sqrt{30}i}{15}\approx 0.730296743i$$

Steps by Finding Square Root

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$15x^{2}=-8$$

Divide both sides by 15.

$$x^{2}=-\frac{8}{15}$$

The equation is now solved.

$$x=\frac{2\sqrt{30}i}{15} x=-\frac{2\sqrt{30}i}{15}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$15x^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 15 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 15\times 8}}{2\times 15}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 15\times 8}}{2\times 15}$$

Multiply -4 times 15.

$$x=\frac{0±\sqrt{-60\times 8}}{2\times 15}$$

Multiply -60 times 8.

$$x=\frac{0±\sqrt{-480}}{2\times 15}$$

Take the square root of -480.

$$x=\frac{0±4\sqrt{30}i}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{0±4\sqrt{30}i}{30}$$

Now solve the equation x=\frac{0±4\sqrt{30}i}{30} when ± is plus.

$$x=\frac{2\sqrt{30}i}{15}$$

Now solve the equation x=\frac{0±4\sqrt{30}i}{30} when ± is minus.

$$x=-\frac{2\sqrt{30}i}{15}$$

The equation is now solved.

$$x=\frac{2\sqrt{30}i}{15} x=-\frac{2\sqrt{30}i}{15}$$