Question

homework assignment 2.5 quadratic equations due friday by 11:59pm points 15 submitting an external tool homework assignment 2.5 quadratic equations score: 4/15 answered: 4/15 question 5 solve the equation 6x^2 + 5x - 4 = 0. answer: x = write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). for example, if you get 4 and -2/3 as your answers, then enter 4,-2/3 in the box. question help: video written example submit question

Explanation:

Step1: Identify coefficients

For the quadratic equation $6x^{2}+5x - 4=0$, we have $a = 6$, $b = 5$, $c=-4$.

Step2: Use quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 6$, $b = 5$, $c=-4$ into it:
First, calculate the discriminant $\Delta=b^{2}-4ac=(5)^{2}-4\times6\times(-4)=25 + 96=121$.
Then, $x=\frac{-5\pm\sqrt{121}}{2\times6}=\frac{-5\pm11}{12}$.

Step3: Find two solutions

When we take the plus - sign: $x_1=\frac{-5 + 11}{12}=\frac{6}{12}=\frac{1}{2}$.
When we take the minus - sign: $x_2=\frac{-5-11}{12}=\frac{-16}{12}=-\frac{4}{3}$.

Answer:

$\frac{1}{2},-\frac{4}{3}$