Giải thích các bước giải:
$\sqrt{5x^2+14x+9}-\sqrt{x^2-x-20}=5\sqrt{x+1}$
$\to \sqrt{5x^2+14x+9}=\sqrt{x^2-x-20}+5\sqrt{x+1}$
$\to 5x^2+14x+9=(\sqrt{x^2-x-20}+5\sqrt{x+1})^2$
$\to 5x^2+14x+9=x^2-x-20+10\sqrt{x^2-x-20}.\sqrt{x+1}+25(x+1)$
$\to 5x^2+14x+9=x^2+24x+5+10\sqrt{x^2-x-20}.\sqrt{x+1}$
$\to 4x^2-10x+4=10\sqrt{x^2-x-20}.\sqrt{x+1}$
$\to 2x^2-5x+2=5\sqrt{x^2-x-20}.\sqrt{x+1}$
$\to (2x^2-5x+2)^2=25(x^2-x-20)(x+1)$
$\to 4x^4-45x^3+33x^2+505x+504=0$
$\to \left(x-8\right)\left(4x+7\right)\left(x^2-5x-9\right)=0$
$\to x=8,x=\dfrac{5+\sqrt{61}}{2}$ vì $5x^2+14x+9, x^2-x-20,x+1\ge 0$
