Answer
$x = -2.64~~$ or $~~x = 1.14$
Work Step by Step
A quadratic equation can be written in this form:
$ax^2 + bx+c = 0$
where $a,b,$ and $c$ are real numbers and $a \neq 0$
We can determine the values of $a, b,$ and $c$:
$2x^2+3x = 6$
$2x^2+3x-6 = 0$
$a = 2$
$b = 3$
$c = -6$
We can use the quadratic formula to find the solutions of the equation:
$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$x = \frac{-(3) \pm \sqrt{(3)^2-(4)(2)(-6)}}{(2)(2)}$
$x = \frac{-3 \pm \sqrt{9+48}}{4}$
$x = \frac{-3 \pm \sqrt{57}}{4}$
$x = \frac{-3 - \sqrt{57}}{4}~~$ or $~~x = \frac{-3 + \sqrt{57}}{4}$
$x = -2.64~~$ or $~~x = 1.14$
