Answer:
Discriminant = 100
Number of solutions = 2
Type of solution = Real and Unique
Rational or Irrational: Rational
Explanation:
Given the quadratic expression;

Rewrite in standard form

Divide through by 2;

From the expression;
a = 1, b = -14 c = 24
Discriminant determines the nature of the root of the quadratic equation;
Discriminant D = b² - 4ac
Substitute the given values;
D = (-14)² - 4(1)(24)
D = 196 - 96
D = 100
Since the discriminant is greater than zero this means that the solution will be real and unique values.
Get the number of solutions;
Using the formula;
x = -b±√D/2a
x = -(-14)±√100/2(1)
x = 14±10/2
x = 14+10/2 and 14-10/2
x = 24/2 and 4/2
x = 12 and 2
Hence the equation has 2 solutions.
The solutions are rational since we can write then as a ratio of two integers