Resolver {c}{y=ax^2+bx+c}{y=x+1}

$$\left. \begin{array} { c } { y = a x ^ { 2 } + b x + c } \\ { y = x + 1 } \end{array} \right.$$

Ebatzi: x, y (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{1-2b+b^{2}+4a-4ac}+b-1}{2a}\text{, }y=-\frac{\sqrt{1-2b+b^{2}+4a-4ac}+b-2a-1}{2a}\text{; }x=-\frac{-\sqrt{1-2b+b^{2}+4a-4ac}+b-1}{2a}\text{, }y=-\frac{-\sqrt{1-2b+b^{2}+4a-4ac}+b-2a-1}{2a}\text{, }&a\neq 0\\x=-\frac{c-1}{b-1}\text{, }y=-\frac{c-b}{b-1}\text{, }&a=0\text{ and }b\neq 1\\x=y-1\text{, }y\in \mathrm{C}\text{, }&a=0\text{ and }b=1\text{ and }c=1\end{matrix}\right.$$

Ebatzi: x, y

$$\left\{\begin{matrix}x=-\frac{\sqrt{1-2b+b^{2}+4a-4ac}+b-1}{2a}\text{, }y=-\frac{\sqrt{1-2b+b^{2}+4a-4ac}+b-2a-1}{2a}\text{; }x=-\frac{-\sqrt{1-2b+b^{2}+4a-4ac}+b-1}{2a}\text{, }y=-\frac{-\sqrt{1-2b+b^{2}+4a-4ac}+b-2a-1}{2a}\text{, }&\left(a\neq 0\text{ and }c=1\right)\text{ or }\left(a\neq 0\text{ and }c>1\text{ and }a\leq -\frac{\left(b-1\right)^{2}}{4\left(1-c\right)}\right)\text{ or }\left(a\neq 0\text{ and }c<1\text{ and }a\geq -\frac{\left(b-1\right)^{2}}{4\left(1-c\right)}\right)\text{ or }\left(c\neq 1\text{ and }a=-\frac{\left(b-1\right)^{2}}{4\left(1-c\right)}\text{ and }b\neq 1\right)\text{ or }\left(b\neq 1\text{ and }a=-\frac{\left(b-1\right)^{2}}{4-4c}\text{ and }c\neq 1\right)\\x=-\frac{c-1}{b-1}\text{, }y=-\frac{c-b}{b-1}\text{, }&a=0\text{ and }b\neq 1\\x=y-1\text{, }y\in \mathrm{R}\text{, }&a=0\text{ and }b=1\text{ and }c=1\end{matrix}\right.$$