Solve: (don't forget about imaginary numbers)
5x^2-7x+12=0
how do I solve this?
please help and thank you
To solve the quadratic equation 5x^2 - 7x + 12 = 0, you can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Where, in our equation, a = 5, b = -7, and c = 12. By plugging in these values into the quadratic formula, we can solve for x.
First, calculate the discriminant (the value inside the square root):
Discriminant, D = b^2 - 4ac
Substituting the values from our equation, we have D = (-7)^2 - 4(5)(12) = 49 - 240 = -191
Since the discriminant is negative, the equation will have complex or imaginary solutions.
Now use the quadratic formula to solve for x:
x = (-(-7) ± √(-191)) / (2(5))
Simplify:
x = (7 ± i√191) / 10
Therefore, the solutions to the equation 5x^2 - 7x + 12 = 0 are:
x = (7 + i√191) / 10 (Complex solution)
x = (7 - i√191) / 10 (Complex solution)