Question

evaluate the discriminant and determine the number and type of solutions to the equation.
$-2d^{2}+6d = 4$
progress: 0/2
part 1 of 2
discriminant: \boxed{}

Explanation:

Step1: Rewrite in standard quadratic form

Subtract 4 from both sides to get $-2d^2 + 6d - 4 = 0$. We can also multiply by -1 to simplify: $2d^2 - 6d + 4 = 0$, where $a=2$, $b=-6$, $c=4$.

Step2: Apply discriminant formula

The discriminant of $ax^2+bx+c=0$ is $\Delta = b^2 - 4ac$. Substitute the values:
$\Delta = (-6)^2 - 4(2)(4)$

Step3: Calculate the discriminant

$\Delta = 36 - 32 = 4$

Step4: Analyze solution type

Since $\Delta > 0$ and is a perfect square, there are 2 distinct real rational solutions.

Answer:

Discriminant: $4$
Number and type of solutions: 2 distinct real rational solutions