Solve 8x^2-5xx+91=0

$$8 x ^ { 2 } - 5 x x + 91 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{273}i}{3}\approx -0-5.507570547i$$

$$x=\frac{\sqrt{273}i}{3}\approx 5.507570547i$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$8x^{2}-5x^{2}+91=0$$

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

$$3x^{2}+91=0$$

Subtract 91 from both sides. Anything subtracted from zero gives its negation.

$$3x^{2}=-91$$

Divide both sides by 3.

$$x^{2}=-\frac{91}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{273}i}{3} x=-\frac{\sqrt{273}i}{3}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$8x^{2}-5x^{2}+91=0$$

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

$$3x^{2}+91=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 91 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 91}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 91}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 91}}{2\times 3}$$

Multiply -12 times 91.

$$x=\frac{0±\sqrt{-1092}}{2\times 3}$$

Take the square root of -1092.

$$x=\frac{0±2\sqrt{273}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{273}i}{6}$$

Now solve the equation x=\frac{0±2\sqrt{273}i}{6} when ± is plus.

$$x=\frac{\sqrt{273}i}{3}$$

Now solve the equation x=\frac{0±2\sqrt{273}i}{6} when ± is minus.

$$x=-\frac{\sqrt{273}i}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{273}i}{3} x=-\frac{\sqrt{273}i}{3}$$