Answer
$x=-\dfrac{3}{2}
\text{ and }
x=\dfrac{1}{2}
$
Work Step by Step
Using the properties of equality, the given equation, $
4x^2+4x=3
,$ is equivalent to
\begin{align*}
4x^2+4x-3=0
\end{align*}
In the equation above, $a=
4
,$ $b=
4
,$ and $c=
-3
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-4\pm\sqrt{4^2-4(4)(-3)}}{2(4)}
\\\\&=
\dfrac{-4\pm\sqrt{16+48}}{8}
\\\\&=
\dfrac{-4\pm\sqrt{64}}{8}
\\\\&=
\dfrac{-4\pm8}{8}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{-4-8}{8} &\text{ OR }& \dfrac{-4+8}{8}
\\\\&
=\dfrac{-12}{8} && =\dfrac{4}{8}
\\\\&
=-\dfrac{3}{2} && =\dfrac{1}{2}
\end{array}
Hence, the solutions are $
x=-\dfrac{3}{2}
\text{ and }
x=\dfrac{1}{2}
.$
