Solve -x^2*48=345

$$- x ^ { 2 } \times 48 = 345$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{115}i}{4}\approx -0-2.680951324i$$

$$x=\frac{\sqrt{115}i}{4}\approx 2.680951324i$$

Steps by Finding Square Root

Divide both sides by 48.

$$-x^{2}=\frac{345}{48}$$

Reduce the fraction \frac{345}{48} to lowest terms by extracting and canceling out 3.

$$-x^{2}=\frac{115}{16}$$

Divide both sides by -1.

$$x^{2}=\frac{\frac{115}{16}}{-1}$$

Express \frac{\frac{115}{16}}{-1} as a single fraction.

$$x^{2}=\frac{115}{16\left(-1\right)}$$

Multiply 16 and -1 to get -16.

$$x^{2}=\frac{115}{-16}$$

Fraction \frac{115}{-16} can be rewritten as -\frac{115}{16} by extracting the negative sign.

$$x^{2}=-\frac{115}{16}$$

The equation is now solved.

$$x=\frac{\sqrt{115}i}{4} x=-\frac{\sqrt{115}i}{4}$$

Steps Using the Quadratic Formula

Divide both sides by 48.

$$-x^{2}=\frac{345}{48}$$

Reduce the fraction \frac{345}{48} to lowest terms by extracting and canceling out 3.

$$-x^{2}=\frac{115}{16}$$

Subtract \frac{115}{16} from both sides.

$$-x^{2}-\frac{115}{16}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -\frac{115}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-\frac{115}{16}\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-\frac{115}{16}\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-\frac{115}{16}\right)}}{2\left(-1\right)}$$

Multiply 4 times -\frac{115}{16}.

$$x=\frac{0±\sqrt{-\frac{115}{4}}}{2\left(-1\right)}$$

Take the square root of -\frac{115}{4}.

$$x=\frac{0±\frac{\sqrt{115}i}{2}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±\frac{\sqrt{115}i}{2}}{-2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{115}i}{2}}{-2} when ± is plus.

$$x=-\frac{\sqrt{115}i}{4}$$

Now solve the equation x=\frac{0±\frac{\sqrt{115}i}{2}}{-2} when ± is minus.

$$x=\frac{\sqrt{115}i}{4}$$

The equation is now solved.

$$x=-\frac{\sqrt{115}i}{4} x=\frac{\sqrt{115}i}{4}$$