SOLUTION: Solve by using the quadratic formula: 4x^2-6x=9. Express roots in EXACT radical form if necessary.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve by using the quadratic formula: 4x^2-6x=9. Express roots in EXACT radical form if necessary.      Log On


   

Question 121030: Solve by using the quadratic formula: 4x^2-6x=9. Express roots in EXACT radical form if necessary.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
To use the quadratic formula, the equation has to be in standard form, thus:

ax%5E2%2Bbx%2Bc=0

Your equation: 4x%5E2-6x=9 has to be re-arranged first.

Add -9 to both sides:

4x%5E2-6x-9=0

Now we have a = 4, b = -6, and c = -9 and we can put these values into the quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A4%2A%28-9%29+%29%29%2F%282%2A4%29+, and simplify
x+=+%286+%2B-+sqrt%28+36%2B144+%29%29%2F8+
x+=+%286+%2B-+sqrt%28+180+%29%29%2F8+

160 = 2 * 2 * 3 * 3 * 5, so sqrt%28180%29=6%2Asqrt%285%29

x+=+%286+%2B-+6%2Asqrt%28+5+%29%29%2F8+

x+=+%283+%2B-+3%2Asqrt%28+5+%29%29%2F4+

Therefore, x=%283%2B3sqrt%285%29%29%2F4 or x=%283-3sqrt%285%29%29%2F4