Answer
The solutions are $x=\dfrac{3}{2}\pm\dfrac{\sqrt{2}}{2}i$
Work Step by Step
$-4x^{2}=-12x+11$
Take all terms to the left side of the equation:
$-4x^{2}+12x-11=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=-4$, $b=12$ and $c=-11$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-12\pm\sqrt{12^{2}-4(-4)(-11)}}{2(-4)}=\dfrac{-12\pm\sqrt{144-176}}{-8}=...$
$...=\dfrac{-12\pm\sqrt{-32}}{-8}=\dfrac{-12\pm4\sqrt{2}i}{-8}=\dfrac{-12}{-8}\pm\dfrac{4\sqrt{2}}{8}i=...$
$...=\dfrac{3}{2}\pm\dfrac{\sqrt{2}}{2}i$
The solutions are $x=\dfrac{3}{2}\pm\dfrac{\sqrt{2}}{2}i$
