If 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

-(-4.5) ±√[(-4.5)² - 4(1.5)(3)]

------------------------------ {substituted into quadratic formula}

2(1.5)

4.5 ± √[20.25 - 18]

------------------- {simplified}

3

4.5 ± √2.25

------------- {simplified}

3

4.5 ± 1.5

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

3

6/3 or 3/3 {evaluated with the ±}

**x = 2 or 1***© Algebra House*
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