Question

What is the solution set of the following equation?

Answer 1

$\dfrac{4}{5}x^2=2x-\dfrac{4}{5}\ \ \ |\cdot5\\\\4x^2=10x-4\ \ \ |-10x\\\\4x^2-10x=-4\ \ \ \ |+4\\\\4x^2-10x+4=0\ \ \ |:2\\\\2x^2-5x+2=0\\\\2x^2-x-4x+2=0\\\\x(2x-1)-2(2x-1)=0\\\\(2x-1)(x-2)=0\iff2x-1=0\ \vee\ x-2=0\\\\x=\dfrac{1}{2}\ \vee\ x=2\\\\Answer:\ \left\{2;\ \dfrac{1}{2}\right\}$