Solve -2d^2-38d+8θ=0

$$- 2 d ^ { 2 } - 38 d + 8 \theta = 0$$

Solve for θ

$$\theta =\frac{d\left(d+19\right)}{4}$$

Steps for Solving Linear Equation

Add 2d^{2} to both sides. Anything plus zero gives itself.

$$-38d+8\theta =2d^{2}$$

Add 38d to both sides.

$$8\theta =2d^{2}+38d$$

Divide both sides by 8.

$$\frac{8\theta }{8}=\frac{2d\left(d+19\right)}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$\theta =\frac{2d\left(d+19\right)}{8}$$

Divide 2d\left(19+d\right) by 8.

$$\theta =\frac{d\left(d+19\right)}{4}$$

Solve for d (complex solution)

$$d=\frac{-\sqrt{16\theta +361}-19}{2}$$

$$d=\frac{\sqrt{16\theta +361}-19}{2}$$

Solve for d

$$d=\frac{-\sqrt{16\theta +361}-19}{2}$$

$$d=\frac{\sqrt{16\theta +361}-19}{2}\text{, }\theta \geq -\frac{361}{16}$$