What are the solutions of the equation, 1.5x²  4.5x = 3 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 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
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