ASMO Math 2022 — Grade 11 — School Round Question 18

You are given $f(x)=\frac{1}{2}[x^2+x-1+|x^2-(x-1)|]$ and $g(x)=7x+20$ for real x. Let $h(x)=f(x)-g(x)$. If $h(x)=0$, express the solutions x in the form $a+b\sqrt{c}$.