Question

solve for u.
$4u^2 = -9u - 2$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

Explanation:

Step1: Rearrange to standard quadratic form

$4u^2 + 9u + 2 = 0$

Step2: Apply quadratic formula

For $au^2+bu+c=0$, $u=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=4$, $b=9$, $c=2$.
$$u=\frac{-9\pm\sqrt{9^2-4(4)(2)}}{2(4)}$$

Step3: Calculate discriminant

$\sqrt{81-32}=\sqrt{49}=7$

Step4: Compute two solutions

$u=\frac{-9+7}{8}=\frac{-2}{8}=-\frac{1}{4}$, $u=\frac{-9-7}{8}=\frac{-16}{8}=-2$

Answer:

$u=-2, -\frac{1}{4}$