Answer
$x=${$\dfrac{-6 \pm 2\sqrt{6}}{3}$}
Work Step by Step
Given: $\dfrac{x^2}{2}+2x+\dfrac{2}{3}=25$
Re-write the equation as: $3x^2+12x+4=0$
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 $x=\dfrac{-(12) \pm \sqrt{(12)^2-4(3)(4)}}{2(3)}$
or, $x=\dfrac{-12 \pm \sqrt{96}}{6}$
or, $x=\dfrac{-12 \pm 4\sqrt{6}}{6}$
Hence, our solution is:
$x=${$\dfrac{-6 \pm 2\sqrt{6}}{3}$}
