Solve the equation: 3x^2=-4x+4 . Fully simplify your answer,including any non-real solutions. x=square

Rearrange the equality<br />$3{x}^{2}+4x-4=0$ <br />Determine the coefficients $a, b, c$ <br />$a=3,b=4,c=-4$ <br />Find the discriminant <br />$\Delta = b^2 - 4ac = {4}^{2}-4\times 3\times (-4) = 52$ <br />Find roots of qudratic equation<br />$\displaystyle \begin{align}&x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}\\&=\frac{-4 \pm \sqrt{{{4}^{2}-4\times 3\times (-4)}}}{2\times 3}\\&=\frac{-4 \pm 2\sqrt{13}}{2\times 3}\\&=\frac{-4 \pm 2\sqrt{13}}{6}\end{align}$ <br />Calculate<br />$\displaystyle x_{1}=-\frac{2}{3}+\frac{1}{3}\sqrt{13},x_{2}=-\frac{2}{3}-\frac{1}{3}\sqrt{13}$ <br />