Answer
The solutions are $x=-\dfrac{11}{4}\pm\dfrac{\sqrt{33}}{4}$
Work Step by Step
$(2x+3)(x+4)=1$
Evaluate the product on the left side:
$2x^{2}+8x+3x+12=1$
Take the $1$ to the left side:
$2x^{2}+8x+3x+12-1=0$
Simplify the left side:
$2x^{2}+11x+11=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
In this case, $a=2$, $b=11$ and $c=11$.
Substitute the known values into the formula and evaluate:
$x=\dfrac{-11\pm\sqrt{11^{2}-4(2)(11)}}{2(2)}=\dfrac{-11\pm\sqrt{121-88}}{4}=...$
$...=\dfrac{-11\pm\sqrt{33}}{4}=-\dfrac{11}{4}\pm\dfrac{\sqrt{33}}{4}$
