Solve 2d^2-d+8=x-3

$$2 d ^ { 2 } - d + 8 = x - 3$$

Solve for x

$$x=2d^{2}-d+11$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$x-3=2d^{2}-d+8$$

Add 3 to both sides.

$$x=2d^{2}-d+8+3$$

Add 8 and 3 to get 11.

$$x=2d^{2}-d+11$$

Solve for d (complex solution)

$$d=\frac{\sqrt{8x-87}+1}{4}$$

$$d=\frac{-\sqrt{8x-87}+1}{4}$$

Solve for d

$$d=\frac{\sqrt{8x-87}+1}{4}$$

$$d=\frac{-\sqrt{8x-87}+1}{4}\text{, }x\geq \frac{87}{8}$$