Solve {l}{x^{2}-(2b-1)x+(b^2-b-20)=0}{3a^2x^2+8abx+4b^2=0,aneq0}

$$\left. \begin{array} { l } { x ^ { 2 } - ( 2 b - 1 ) x + ( b ^ { 2 } - b - 20 ) = 0 } \\ { 3 a ^ { 2 } x ^ { 2 } + 8 a b x + 4 b ^ { 2 } = 0 , a \neq 0 } \end{array} \right.$$

Evaluate (complex solution)

$$\left(x-b-4\right)\left(x-b+5\right)=0,\ \left(3ax+2b\right)\left(ax+2b\right)=0,\ a\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=\frac{8}{a+2}\text{, }&a\neq 0\text{ and }b=-\frac{4a}{a+2}\text{ and }a\neq -2\\x=\frac{8}{3a+2}\text{, }&a\neq 0\text{ and }b=-\frac{12a}{3a+2}\text{ and }a\neq -\frac{2}{3}\\x=-\frac{10}{a+2}\text{, }&a\neq 0\text{ and }b=\frac{5a}{a+2}\text{ and }a\neq -2\\x=-\frac{10}{3a+2}\text{, }&a\neq 0\text{ and }b=\frac{15a}{3a+2}\text{ and }a\neq -\frac{2}{3}\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\frac{5a}{a+2}\text{, }&a\neq 0\text{ and }x=-\frac{10}{a+2}\text{ and }a\neq -2\\b=\frac{15a}{3a+2}\text{, }&a\neq 0\text{ and }x=-\frac{10}{3a+2}\text{ and }a\neq -\frac{2}{3}\\b=-\frac{4a}{a+2}\text{, }&a\neq 0\text{ and }x=\frac{8}{a+2}\text{ and }a\neq -2\\b=-\frac{12a}{3a+2}\text{, }&a\neq 0\text{ and }x=\frac{8}{3a+2}\text{ and }a\neq -\frac{2}{3}\end{matrix}\right.$$