Solve 5x^2+8*+3=0

$$5 { x }^{ 2 } +8 \times +3=0$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{30}i}{5}\approx -0-2.19089023i$$

$$x=\frac{2\sqrt{30}i}{5}\approx 2.19089023i$$

Steps by Finding Square Root

Multiply 8 and 3 to get 24.

$$5x^{2}+24=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$5x^{2}=-24$$

Divide both sides by 5.

$$x^{2}=-\frac{24}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{30}i}{5} x=-\frac{2\sqrt{30}i}{5}$$

Steps Using the Quadratic Formula

Multiply 8 and 3 to get 24.

$$5x^{2}+24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 24}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 24}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 24}}{2\times 5}$$

Multiply -20 times 24.

$$x=\frac{0±\sqrt{-480}}{2\times 5}$$

Take the square root of -480.

$$x=\frac{0±4\sqrt{30}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±4\sqrt{30}i}{10}$$

Now solve the equation x=\frac{0±4\sqrt{30}i}{10} when ± is plus.

$$x=\frac{2\sqrt{30}i}{5}$$

Now solve the equation x=\frac{0±4\sqrt{30}i}{10} when ± is minus.

$$x=-\frac{2\sqrt{30}i}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{30}i}{5} x=-\frac{2\sqrt{30}i}{5}$$