Solve x^3+(a-5)x^2+(4-3a)x+a^2-aleq0

$$x ^ { 3 } + ( a - 5 ) x ^ { 2 } + ( 4 - 3 a ) x + a ^ { 2 } - a \leq 0$$

Solve for x

$$\left\{\begin{matrix}\\x=\sqrt{4-a}+2\text{, }&\text{unconditionally}\\x=1-a\text{, }&a\neq 4\\x\in \begin{bmatrix}1-a,\sqrt{4-a}+2\end{bmatrix}\text{, }&a\geq \frac{-\sqrt{21}-3}{2}\text{ and }a\leq \frac{\sqrt{21}-3}{2}\\x\in \begin{bmatrix}-\sqrt{4-a}+2,\sqrt{4-a}+2\end{bmatrix}\text{, }&a>\frac{\sqrt{21}-3}{2}\text{ and }a<4\\x=2\text{, }&a\geq -1\text{ and }a\leq 4\\x\leq 1-a\text{, }&a\geq 4\text{ or }\left(a\geq \frac{\sqrt{21}-3}{2}\text{ and }a<4\right)\\x\leq -\sqrt{4-a}+2\text{, }&\left(a>\frac{-\sqrt{21}-3}{2}\text{ and }a<\frac{\sqrt{21}-3}{2}\right)\text{ or }a\leq -1\\x\leq -3\text{, }&\left(a\geq \frac{\sqrt{21}-3}{2}\text{ and }a\leq 4\right)\text{ or }\left(a>\frac{-\sqrt{21}-3}{2}\text{ and }a<\frac{\sqrt{21}-3}{2}\right)\text{ or }\left(a\geq -21\text{ and }a\leq -1\right)\\x\in \begin{bmatrix}\sqrt{4-a}+2,1-a\end{bmatrix}\text{, }&a\leq \frac{-\sqrt{21}-3}{2}\\x=-\sqrt{4-a}+2\text{, }&a<4\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}\\a\in \begin{bmatrix}\frac{-\sqrt{x^{4}-10x^{3}+27x^{2}-10x+1}-x^{2}+3x+1}{2},\frac{\sqrt{x^{4}-10x^{3}+27x^{2}-10x+1}-x^{2}+3x+1}{2}\end{bmatrix}\text{, }&\text{unconditionally}\\a=\frac{-\sqrt{21}-3}{2}\text{, }&x\neq \frac{5-\sqrt{21}}{2}\text{ and }\frac{-\sqrt{21}-3}{2}\leq \frac{\sqrt{x^{4}-10x^{3}+27x^{2}-10x+1}-x^{2}+3x+1}{2}\text{ and }\frac{-\sqrt{21}-3}{2}\geq \frac{-\sqrt{x^{4}-10x^{3}+27x^{2}-10x+1}-x^{2}+3x+1}{2}\\a=\frac{\sqrt{21}-3}{2}\text{, }&x\neq \frac{\sqrt{21}+5}{2}\text{ and }\frac{\sqrt{21}-3}{2}\leq \frac{\sqrt{x^{4}-10x^{3}+27x^{2}-10x+1}-x^{2}+3x+1}{2}\text{ and }\frac{\sqrt{21}-3}{2}\geq \frac{-\sqrt{x^{4}-10x^{3}+27x^{2}-10x+1}-x^{2}+3x+1}{2}\end{matrix}\right.$$