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# solution of the equation

Determine the nature of the solutions of the equation:
5x^2-6x=-9

a)Two real solutions
b) No solutions
c)One real solution
d)two solutions with imaginary parts

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
1
5X^2 -6X + 9 =0

Test :

b^2 - 4ac= 6^2 - 4 ( 5) ( 9) = 36 - 180 = - 144

Discriminant is negative, therefore 2 complex roots. Roots with Imaginary parts.

So, you know which answer you should mark as the correct answer.
Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (438 lesson ratings) (438)
1
5x2 - 6x = -9

Put the equation in standard form:

5x2 - 6x + 9 = 0

Use the quadratic formula to find the values of x:

x = (-b/2a) ± (1/2a) √(b2-4ac)

For this problem, a = 5, b = -6, c = 9:

x = (6/10) ± (1/10)√[(-6)2-4(5)(9)]

x = (3/5) ± (1/10)√(36-180)

x = (6/10) ± (1/10)√(-144)

Can you finish it from here?