Riješi 16K^2(a^2+a)+5a^2+2a=3

$$16 K ^ { 2 } ( a ^ { 2 } + a ) + 5 a ^ { 2 } + 2 a = 3$$

Izračunaj K (complex solution)

$$\left\{\begin{matrix}K=-\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{; }K=\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{, }&a\neq 0\\K\in \mathrm{C}\text{, }&a=-1\end{matrix}\right,$$

Izračunaj a (complex solution)

$$\left\{\begin{matrix}\\a=-1\text{, }&\text{unconditionally}\\a=\frac{3}{16K^{2}+5}\text{, }&K\neq -\frac{\sqrt{5}i}{4}\text{ and }K\neq \frac{\sqrt{5}i}{4}\end{matrix}\right,$$

Izračunaj K

$$\left\{\begin{matrix}K=\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{; }K=-\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{, }&a>0\text{ and }a\leq \frac{3}{5}\\K\in \mathrm{R}\text{, }&a=-1\end{matrix}\right,$$

Izračunaj a

$$a=-1$$

$$a=\frac{3}{16K^{2}+5}$$