Question 197469
{{{ x^2 + 3/2x = 3}}}
Complete the square
{{{x^2 + (3/2)*x + (3/4)^2 = 3 + (3/4)^2}}}
{{{x^2 + (3/2)*x + 9/16 = 48/16 + 9/16}}}
The left side is a perfect square
{{{(x + (3/4))^2 = 57/16}}}
Take the square root of both sides
{{{x + 3/4 =  0 +- sqrt(57)/4}}}
{{{x = (-3 + sqrt(57)) / 4}}}
and
{{{x = (-3 - sqrt(57)) / 4}}}
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I checked one solution with pencil&paper
OK