What are the

*solutions*of the equation, 1.5x² - 4.5x = -3If it is difficult to factor, the quadratic formula will always work:

1.5x² - 4.5x = -3

1.5x² - 4.5x + 3 = 0 {added 3 to both sides}

a = 1.5, b = -4.5, c = 3

-b ± √[b² - 4ac]

--------------------- = x {the quadratic formula}

2a

-(-4.5) ±√[(-4.5)² - 4(1.5)(3)]

-------------------------------------- = x {substituted into quadratic formula}

2(1.5)

4.5 ± √[20.25 - 18]

------------------------- = x {simplified}

3

4.5 ± √2.25

--------------- = x {simplified}

3

4.5 ± 1.5

------------- = x {evaluated square root of 2.25}

3

6/3 or 3/3 {evaluated with the ±}

**x = 2 or 1**

*- Algebra House*