Question

3x.(x-2)=2. (x+3/2) em baskara

Answer 1

$3x(x-2) = \not2 \left( \dfrac{x+3}{\not2} \right) \to\\\\ 3x^2 - 6x = x+3\to\\\\ 3x^2-6x-x-3=0\to\\\\ 3x^2-7x-3 = 0\\\\a=3~~;~~b=-7~~;~~c=-3\\\\ \Delta=b^2-4ac\to \Delta=(-7)^2-4.3.(-3)\to \Delta=49+36\to \underline{\Delta=85}$


$x = \dfrac{-b \pm \sqrt{ \Delta} }{2a} \to~~~~ x = \dfrac{-(-7) \pm \sqrt{ 85} }{2.3} \to~~~~ x = \dfrac{7 \pm \sqrt{ 85} }{6} \to\\\\\\ x' = \dfrac{7 + \sqrt{ 85} }{6} ~~~~ou~~~~x' \approx 2,7\\\\\\ x'' = \dfrac{7 - \sqrt{ 85} }{6} ~~~~ou~~~~x'' \approx -0,37$




$\large\boxed{\boxed{S= \left\{ \dfrac{7 - \sqrt{ 85} }{6} ~~;~~\dfrac{7 + \sqrt{ 85} }{6}\right\}}}\\\\\\ou\\\\\\ \large\boxed{\boxed{S= \left\{ -0,37~~;~~2,7 \right\}}}$