Answer
$x = -0.92~~$ or $~~x = 1.52$
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 $c$:
$5x^2 = 3x+7$
$5x^2 -3x-7 = 0$
$a = 5$
$b = -3$
$c = -7$
We can use the quadratic formula to find the solutions of the equation:
$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$x = \frac{-(-3) \pm \sqrt{(-3)^2-(4)(5)(-7)}}{(2)(5)}$
$x = \frac{3 \pm \sqrt{9+140}}{10}$
$x = \frac{3 \pm \sqrt{149}}{10}$
$x = \frac{3 - \sqrt{149}}{10}~~$ or $~~x = \frac{3 + \sqrt{149}}{10}$
$x = -0.92~~$ or $~~x = 1.52$
