Solve 2x^2+3x+a+1=0

$$2 x ^ { 2 } + 3 x + a + 1 = 0$$

Solve for a

$$a=-\left(x+1\right)\left(2x+1\right)$$

Solution Steps

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

$$3x+a+1=-2x^{2}$$

Subtract 3x from both sides.

$$a+1=-2x^{2}-3x$$

Subtract 1 from both sides.

$$a=-2x^{2}-3x-1$$

Solve for x (complex solution)

$$x=\frac{\sqrt{1-8a}-3}{4}$$

$$x=\frac{-\sqrt{1-8a}-3}{4}$$

Solve for x

$$x=\frac{\sqrt{1-8a}-3}{4}$$

$$x=\frac{-\sqrt{1-8a}-3}{4}\text{, }a\leq \frac{1}{8}$$