Question

2° DADA A EQUAÇÃO:
$\frac{2x}{4} - \frac{5}{3} = x - \frac{7}{x}$
CALCULE O VALOR DE X

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Answer 1

$\large\boxed{\begin{array}{l}\rm\dfrac{2x}{4}-\dfrac{5}{3}=x-\dfrac{7}{x}\bullet(12x)\\\\\rm6x^2-20x=12x^2-84\\\rm 6x^2-12x^2-20x+84=0\\\rm -6x^2-20x+84=0\div(-2)\end{array}}$

$\large\boxed{\begin{array}{l}\rm 3x^2+10x-42=0\\\rm\Delta=b^2-4ac\\\rm\Delta=10^2-4\cdot3\cdot(-42)\\\rm\Delta=100+504\\\rm\Delta=604\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-10\pm\sqrt{604}}{2\cdot3}\\\\\rm x=\dfrac{-10\pm2\sqrt{151}}{6}\begin{cases}\rm x_1=\dfrac{-10+2\sqrt{151}}{6}=\dfrac{-5+\sqrt{151}}{3}\\\\\rm x_2=\dfrac{-10-2\sqrt{151}}{6}=\dfrac{-5-\sqrt{151}}{3}\end{cases}\end{array}}$