Answer
The solutions are $x=-\dfrac{1}{3}\pm\dfrac{\sqrt{14}}{3}i$
Work Step by Step
$-x(3x+2)=5$
Evaluate the product on the left side:
$-3x^{2}-2x=5$
Take all terms to the right side and rearrange:
$0=3x^{2}+2x+5$
$3x^{2}+2x+5=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=3$, $b=2$ and
$c=5$.
Substitute the known values into the formula and evaluate:
$x=\dfrac{-2\pm\sqrt{2^{2}-4(3)(5)}}{2(3)}=\dfrac{-2\pm\sqrt{4-60}}{6}=\dfrac{-2\pm\sqrt{-56}}{6}=...$
$...=\dfrac{-2\pm2\sqrt{14}i}{6}=-\dfrac{2}{6}\pm\dfrac{2\sqrt{14}}{6}i=-\dfrac{1}{3}\pm\dfrac{\sqrt{14}}{3}i$
The solutions are $x=-\dfrac{1}{3}\pm\dfrac{\sqrt{14}}{3}i$
