how can you solved this problem-3n squared+5n-2=0 using discriminant and to know if it is 1 or sol

To solve the quadratic equation -3n^2 + 5n - 2 = 0 using the discriminant, D, we need to follow these steps:

Step 1: Identify the coefficients of the quadratic equation.
- In this case, a = -3, b = 5, and c = -2.

Step 2: Calculate the discriminant using the formula D = b^2 - 4ac.
- In this case, D = (5)^2 - 4(-3)(-2).

Step 3: Simplify the expression for the discriminant.
- D = 25 - 24 = 1

Step 4: Analyze the value of the discriminant to determine the nature of the roots.
- If D > 0, the quadratic equation has two distinct real roots.
- If D = 0, the quadratic equation has one real root (also known as a repeated root or a perfect square trinomial).
- If D < 0, the quadratic equation has no real roots, only complex roots.

In this case, the value of the discriminant D is 1, which is greater than zero (D > 0). Therefore, the quadratic equation has two distinct real roots.

To find the roots of the quadratic equation, we can use the quadratic formula:

n = (-b ± √D) / (2a).

Substituting the values for a, b, and D, we get:

n = (-5 ± √1) / (2(-3)).

Simplifying further:

n = (-5 ± 1) / (-6).

This leads to two possible values for n:

n₁ = (-5 + 1) / -6 = -4/6 = -2/3.
n₂ = (-5 - 1) / -6 = -6/6 = -1.

Therefore, the solutions to the quadratic equation -3n^2 + 5n - 2 = 0 are n = -2/3 and n = -1.