Solve 34div5*x^2+8.16=0

$$34 \div 5 \times { x }^{ 2 } +8.16=0$$

Solve for x (complex solution)

$$x=-\frac{i\sqrt{30}}{5}\approx -0-1.095445115i$$

$$x=\frac{i\sqrt{30}}{5}\approx 1.095445115i$$

Steps by Finding Square Root

Subtract 8.16 from both sides. Anything subtracted from zero gives its negation.

$$\frac{34}{5}x^{2}=-8.16$$

Multiply both sides by \frac{5}{34}, the reciprocal of \frac{34}{5}.

$$x^{2}=-8.16\times \frac{5}{34}$$

Multiply -8.16 and \frac{5}{34} to get -\frac{6}{5}.

$$x^{2}=-\frac{6}{5}$$

The equation is now solved.

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

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.

$$\frac{34}{5}x^{2}+8.16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{34}{5} for a, 0 for b, and 8.16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{34}{5}\times 8.16}}{2\times \frac{34}{5}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{34}{5}\times 8.16}}{2\times \frac{34}{5}}$$

Multiply -4 times \frac{34}{5}.

$$x=\frac{0±\sqrt{-\frac{136}{5}\times 8.16}}{2\times \frac{34}{5}}$$

Multiply -\frac{136}{5} times 8.16 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{-\frac{27744}{125}}}{2\times \frac{34}{5}}$$

Take the square root of -\frac{27744}{125}.

$$x=\frac{0±\frac{68\sqrt{30}i}{25}}{2\times \frac{34}{5}}$$

Multiply 2 times \frac{34}{5}.

$$x=\frac{0±\frac{68\sqrt{30}i}{25}}{\frac{68}{5}}$$

Now solve the equation x=\frac{0±\frac{68\sqrt{30}i}{25}}{\frac{68}{5}} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{68\sqrt{30}i}{25}}{\frac{68}{5}} when ± is minus.

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

The equation is now solved.

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