Solve 9/2d^2+6=4

$$\frac { 9 } { 2 } d ^ { 2 } + 6 = 4$$

Solve for d

$$d=-\frac{2}{3}i\approx -0.666666667i$$

$$d=\frac{2}{3}i\approx 0.666666667i$$

Steps by Finding Square Root

Subtract 6 from both sides.

$$\frac{9}{2}d^{2}=4-6$$

Subtract 6 from 4 to get -2.

$$\frac{9}{2}d^{2}=-2$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$d^{2}=-2\times \frac{2}{9}$$

Multiply -2 and \frac{2}{9} to get -\frac{4}{9}.

$$d^{2}=-\frac{4}{9}$$

The equation is now solved.

$$d=\frac{2}{3}i d=-\frac{2}{3}i$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$\frac{9}{2}d^{2}+6-4=0$$

Subtract 4 from 6 to get 2.

$$\frac{9}{2}d^{2}+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{9}{2} for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\times \frac{9}{2}\times 2}}{2\times \frac{9}{2}}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times \frac{9}{2}\times 2}}{2\times \frac{9}{2}}$$

Multiply -4 times \frac{9}{2}.

$$d=\frac{0±\sqrt{-18\times 2}}{2\times \frac{9}{2}}$$

Multiply -18 times 2.

$$d=\frac{0±\sqrt{-36}}{2\times \frac{9}{2}}$$

Take the square root of -36.

$$d=\frac{0±6i}{2\times \frac{9}{2}}$$

Multiply 2 times \frac{9}{2}.

$$d=\frac{0±6i}{9}$$

Now solve the equation d=\frac{0±6i}{9} when ± is plus.

$$d=\frac{2}{3}i$$

Now solve the equation d=\frac{0±6i}{9} when ± is minus.

$$d=-\frac{2}{3}i$$

The equation is now solved.

$$d=\frac{2}{3}i d=-\frac{2}{3}i$$