Solve y+6+1/16=2x^2+x+1/16

$$y+6+ \frac{ 1 }{ 16 } = 2 { x }^{ 2 } +x+ \frac{ 1 }{ 16 }$$

Solve for y

$$y=\left(2x-3\right)\left(x+2\right)$$

Solution Steps

Add 6 and \frac{1}{16} to get \frac{97}{16}.

$$y+\frac{97}{16}=2x^{2}+x+\frac{1}{16}$$

Subtract \frac{97}{16} from both sides.

$$y=2x^{2}+x+\frac{1}{16}-\frac{97}{16}$$

Subtract \frac{97}{16} from \frac{1}{16} to get -6.

$$y=2x^{2}+x-6$$

Solve for x (complex solution)

$$x=\frac{\sqrt{8y+49}-1}{4}$$

$$x=\frac{-\sqrt{8y+49}-1}{4}$$

Solve for x

$$x=\frac{\sqrt{8y+49}-1}{4}$$

$$x=\frac{-\sqrt{8y+49}-1}{4}\text{, }y\geq -\frac{49}{8}$$