Solve for u. 3u^(2)=-7u-4

Rearrange equation to set zero: Step 1: Rearrange the equation to set it to zero. Move all terms to one side of the equation to form a standard quadratic equation. 3u^2 + 7u + 4 = 0Use quadratic formula to solve: Step 2: Use the quadratic formula to solve for u. The quadratic formula is u = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = 3, b = 7, and c = 4. u = (-(7) ± sqrt((7)^2 - 4*3*4)) / (2*3)Calculate the discriminant: Step 3: Calculate the discriminant (b^2 - 4ac). Discriminant = (7)^2 - 4*3*4 = 49 - 48 = 1Substitute back into formula: Step 4: Substitute the discriminant back into the quadratic formula. u = (-7 ± sqrt(1)) / 6 u = (-7 ± 1) / 6Solve for possible values: Step 5: Solve for the two possible values of u. u = (-7 + 1) / 6 = -6 / 6 = -1 u = (-7 - 1) / 6 = -8 / 6 = -4/3

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Q. Solve for

u

\newline

3 u^{2}=-7 u-4

Rearrange equation to set zero: Step $1$ : Rearrange the equation to set it to zero. $\newline$ Move all terms to one side of the equation to form a standard quadratic equation. $\newline$ $3u^2 + 7u + 4 = 0$
Use quadratic formula to solve: Step $2$ : Use the quadratic formula to solve for $u$ . The quadratic formula is $u = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 3$ , $b = 7$ , and $c = 4$ . $u = \frac{-(7) \pm \sqrt{(7)^2 - 4\cdot3\cdot4}}{2\cdot3}$
Calculate the discriminant: Step $3$ : Calculate the discriminant $(b^2 - 4ac)$ . $\newline$ Discriminant = $(7)^2 - 4\cdot3\cdot4 = 49 - 48 = 1$
Substitute back into formula: Step $4$ : Substitute the discriminant back into the quadratic formula. $\newline$ $u = \frac{-7 \pm \sqrt{1}}{6}$ $\newline$ $u = \frac{-7 \pm 1}{6}$
Solve for possible values: Step $5$ : Solve for the two possible values of $u$ . $u = \frac{{-7 + 1}}{{6}} = \frac{{-6}}{{6}} = -1$ $u = \frac{{-7 - 1}}{{6}} = \frac{{-8}}{{6}} = -\frac{4}{3}$