Solve D=left(9x-4right)^2-121

$$D = { \left(9x-4 \right) }^{ 2 } -121$$

Solve for D

$$D=81x^{2}-72x-105$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9x-4\right)^{2}.

$$D=81x^{2}-72x+16-121$$

Subtract 121 from 16 to get -105.

$$D=81x^{2}-72x-105$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{D+121}+4}{9}$$

$$x=\frac{\sqrt{D+121}+4}{9}$$

Solve for x

$$x=\frac{-\sqrt{D+121}+4}{9}$$

$$x=\frac{\sqrt{D+121}+4}{9}\text{, }D\geq -121$$