Answer
$x=${$1,\dfrac{5 }{7}$}
Work Step by Step
Given: $7x(x-2)=3-2(x+4)$
Re-write the given equation as: $7x^2-14x=3-2x-8$
This implies that $7x^2-12x+5=0$
Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
This implies that $x=\dfrac{-(-12) \pm \sqrt{(-12)^2-4(7)(5)}}{2(7)}$
or, $x=\dfrac{12 \pm \sqrt {4}}{14}$
or, $x=${$\dfrac{12+- 2}{14},\dfrac{12-2}{14}$}
Hence, our solution set is: $x=${$1,\dfrac{5 }{7}$}
