## Algebra 2 Common Core

$x=\left\{ -\dfrac{8}{3}, 1 \right\}$
Using the properties of equality, the given equation, $3x^2+5x=8 ,$ is equivalent to \begin{align*} 3x^2+5x-8&=8-8 \\ 3x^2+5x-8&=0 .\end{align*} Using $ax^2+bx+c=0,$ the equation above has $a= 3 ,$ $b= 5 ,$ and $c= -8 .$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then \begin{align*} x&=\dfrac{-5\pm\sqrt{5^2-4(3)(-8)}}{2(3)} \\\\&= \dfrac{-5\pm\sqrt{25+96}}{6} \\\\&= \dfrac{-5\pm\sqrt{121}}{6} \\\\&= \dfrac{-5\pm11}{6} \end{align*} \begin{array}{lcl} x=\dfrac{-5-11}{6} &\text{ OR }& x=\dfrac{-5+11}{6} \\\\ x=\dfrac{-16}{6} && x=\dfrac{6}{6} \\\\ x=-\dfrac{8}{3} && x=1 .\end{array} The solutions are $x=\left\{ -\dfrac{8}{3}, 1 \right\} .$