Atrisiniet frac{5(4x+1)^frac{3{2}}}{6}+c=-1/4

$$\frac { 5 ( 4 x + 1 ) ^ { \frac { 3 } { 2 } } } { 6 } + c = \frac { - 1 } { 4 }$$

Atrast c (complex solution)

$$c=-\frac{5\left(4x+1\right)^{\frac{3}{2}}}{6}-\frac{1}{4}$$

Atrast x (complex solution)

$$x=\frac{9c^{2}}{25}+\frac{9c}{50}-\frac{91}{400}$$

$$c=-\frac{1}{4}\text{ or }arg(\frac{6c}{5}+\frac{3}{10})\geq \pi$$

Atrast c

$$c=-\frac{5\left(4x+1\right)^{\frac{3}{2}}}{6}-\frac{1}{4}$$

$$x\geq -\frac{1}{4}$$

Atrast x

$$x=\frac{\sqrt[3]{10}\left(12c+3\right)^{\frac{2}{3}}}{40}-\frac{1}{4}$$

$$-\frac{6c}{5}-\frac{3}{10}\geq 0$$