Intermediate Algebra for College Students (7th Edition)

{$\dfrac{-11 - \sqrt {33}}{4},\dfrac{-11 + \sqrt {33}}{4}$}
Given: $(2x+3)(x+4)=0$ Re-write the given equation as: $2x^2+11x+11=0$ Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ This implies that $x=\dfrac{-(11) \pm \sqrt{(11)^2-4(2)(11)}}{2(2)}$ or, $x=\dfrac{-11 \pm \sqrt {33}}{4}$ or, $x=\dfrac{-11 - \sqrt {33}}{4},\dfrac{-11 + \sqrt {33}}{4}$ Hence, our solution set is: {$\dfrac{-11 - \sqrt {33}}{4},\dfrac{-11 + \sqrt {33}}{4}$}