Answer :
ANSWER:
-1 and -2/3
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]-3x^2\: -\: 5x\: +\: 2\: =\: 4[/tex]We rearrange the equation and it looks like this:
[tex]\begin{gathered} -3x^2\: -\: 5x\: +\: 2\: -4=\: 4-4 \\ -3x^2\: -\: 5x\: -2=0 \end{gathered}[/tex]We apply the quadratic formula which is the following:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{ in this case} \\ a=-3 \\ b=-5 \\ c=-2 \end{gathered}[/tex]we replace and calculate the values of x:
[tex]\begin{gathered} x_{1,2}=\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot(-3)\cdot(-2)}}{2\cdot(-3)} \\ x_{1,2}=\frac{5\pm1}{-6} \\ x_1=\frac{5+1}{-6}=\frac{6}{-6}=-1 \\ x_2=\frac{5-1}{-6}=\frac{4}{-6}=-\frac{2}{3} \end{gathered}[/tex]Therefore the solution of the equation is -1 and -2/3