Question

Решите уравнение. 6x^2-5x-1=0

Answer 1

6x²-5x-1=0
I способ:
a+b+c=0 (6-5-1=0) ⇒ x=1, x=-1/6
II способ:
D=(-5)²-4*6*(-1)=25+24=49=7²
x=(5+7)/2*6=12/12=1
x=(5-7)/2*6=-2/12=-1/6

Answer 2

I can help you solve quadratic equations. A quadratic equation is an equation that has a term with x^2, such as 6x^2-5x-1=0. There are different methods to solve quadratic equations, such as factoring, using the quadratic formula, or completing the square.

Since the user asked for a detailed answer, I will explain how to use the quadratic formula, which is a general method that works for any quadratic equation. The quadratic formula is:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. In this case, a = 6, b = -5, and c = -1. To use the quadratic formula, we need to substitute these values and simplify the expression. Here are the steps:

$$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(6)(-1)}}{2(6)}$$

$$x = \frac{5 \pm \sqrt{25 + 24}}{12}$$

$$x = \frac{5 \pm \sqrt{49}}{12}$$

$$x = \frac{5 \pm 7}{12}$$

$$x = \frac{5 + 7}{12} \text{ or } x = \frac{5 - 7}{12}$$

$$x = 1 \text{ or } x = -\frac{1}{6}$$

These are the two solutions of the quadratic equation. You can check them by plugging them back into the original equation and verifying that they make it true.

I hope this helps you understand how to solve quadratic equations using the quadratic formula. If you want to learn more about other methods or practice some examples, you can visit these websites: [4 ways to solve quadratic equations](https://www.wikihow.com/Solve-Quadratic-Equations), [Solving quadratic equations by factoring](https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratics-solve-factoring/a/solving-quadratic-equations-by-factoring), [How to solve quadratic equations (4 methods to know)](https://jdmeducational.com/how-to-solve-quadratic-equations-4-methods-to-know/), [Solving quadratic equations - CliffsNotes](https://www.cliffsnotes.com/study-guides/algebra/algebra-i/quadratic-equations/solving-quadratic-equations).