Question

solve for u.

$2u^2 - 7u = 4$

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

We start with the equation \(2u^{2}-7u = 4\). Subtract 4 from both sides to get the quadratic equation in standard form \(ax^{2}+bx + c=0\). So we have \(2u^{2}-7u - 4=0\). Here, \(a = 2\), \(b=- 7\), and \(c=-4\).

Step2: Use the quadratic formula

The quadratic formula is \(u=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Substitute the values of \(a\), \(b\), and \(c\) into the formula. First, calculate the discriminant \(\Delta=b^{2}-4ac=(-7)^{2}-4\times2\times(-4)=49 + 32=81\). Then, \(u=\frac{-(-7)\pm\sqrt{81}}{2\times2}=\frac{7\pm9}{4}\).

Step3: Find the two solutions

For the plus sign: \(u=\frac{7 + 9}{4}=\frac{16}{4}=4\). For the minus sign: \(u=\frac{7-9}{4}=\frac{-2}{4}=-\frac{1}{2}\).

Answer:

\(4,-\frac{1}{2}\)