\(\frac{{x}^{2}+x+3}{{2x}^{2}+x-6}≥0\)
\(\frac{{x}^{2}+x+3}{{2x}^{2}+x-6}\times({2x}^{2}+x-6)≥0\times({2x}^{2}+x-6)\)
\(\frac{({x}^{2}+x+3)({2x}^{2}+x-6)}{{2x}^{2}+x-6}≥0\times({2x}^{2}+x-6)\)
\({x}^{2}+x+3≥0\times({2x}^{2}+x-6)\)
\({x}^{2}+x+3≥0\)
\(x ≥ {-1 \pm \sqrt{1^2-4(1)(3)} \over 2(1)}\)
\(x ≥ {-1 \pm \sqrt{1-4(1)(3)} \over 2(1)}\)
\(x ≥ {-1 \pm \sqrt{1-4(3)} \over 2(1)}\)
\(x ≥ {-1 \pm \sqrt{1-12} \over 2(1)}\)
\(x ≥ {-1 \pm \sqrt{-11} \over 2(1)}\)
\(x ≥ {-1 \pm \sqrt{11}i \over 2(1)}\)
\(x ≥ {-1 \pm \sqrt{11}i \over 2}\)
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