Question

solve for v.

$2v^2 - 2 = 3v$

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

$2v^2 - 3v - 2 = 0$

Step2: Apply quadratic formula $v=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, $a=2$, $b=-3$, $c=-2$.
$$v=\frac{3\pm\sqrt{(-3)^2-4(2)(-2)}}{2(2)}$$

Step3: Calculate discriminant

$\sqrt{9 + 16} = \sqrt{25} = 5$

Step4: Compute two solutions

$v_1=\frac{3+5}{4}=\frac{8}{4}=2$, $v_2=\frac{3-5}{4}=\frac{-2}{4}=-\frac{1}{2}$

Answer:

$2, -\frac{1}{2}$