Answer
$x = \frac{3}{4}$ or $x=1$
Work Step by Step
We are asked to solve this equation using the quadratic formula, which is given by:
$x = \frac{-b ± \sqrt {b^2 - 4ac}}{2a}$
where $a$ is the coefficient of the first term, $b$ is the coefficient of the 1st degree term, and $c$ is the constant.
Let's plug in the numbers from our equation into the formula:
$x = \dfrac{-7 ± \sqrt {7^2 - 4(-4)(-3)}}{2(-4)}$
Let's simplify:
$x = \dfrac{-7 ± \sqrt {49 - 48}}{-8}$
Let's simplify what is inside the radical:
$x = \dfrac{-7 ± \sqrt {1}}{-8}$
Simplify the radical:
$x = \dfrac{-7 ± 1}{-8}$
Split the solution into two fractions:
$x = \dfrac{-6}{-8}$ or $x = \dfrac{-8}{-8}$
Simplify the fractions to solve:
$x = \frac{3}{4}, 1$
