Consider the following quadratic equation:
−2y^2+6=−5y
Step 2 of 2 : Use the discriminant, b2−4ac
, to determine the number of solutions of the given quadratic equation. Then solve the quadratic equation using the formula y=−b±b2−4ac⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯/2a
.
The given quadratic equation is -2y^2 + 6 = -5y.
To determine the number of solutions, we need to calculate the discriminant, which is b^2 - 4ac.
In this case, a = -2, b = -5, and c = 6.
Substituting these values into the discriminant formula:
Discriminant = (-5)^2 - 4(-2)(6)
= 25 + 48
= 73
Since the discriminant is positive and greater than 0 (73 > 0), the quadratic equation has 2 distinct solutions.
Now, let's solve the quadratic equation using the formula:
y = (-(-5) ± √(b^2 - 4ac)) / (2a)
= (5 ± √(73)) / (-4)
Therefore, the solutions to the quadratic equation -2y^2 + 6 = -5y are:
y = (5 + √73) / -4
and
y = (5 - √73) / -4