Solve using formula. y^2+1 3 y=2 - Vidyadip

Question

Solve using formula.
$y^2+\frac{1}{3} y=2$

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Answer

$\begin{array}{l}3 y^2+y-6=0 \\ \Rightarrow 3 y^2+y-6=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=3, b=1 \text { and } c=-6 \\ \therefore b^2-4 a c=1^2-4(3)(-6) \\ =1+72 \\ =73 \\ Y=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\end{array}$
$\begin{array}{l}\Rightarrow y=\frac{-1 \pm \sqrt{73}}{2 \times 3} \\ \Rightarrow y=\frac{-1 \pm \sqrt{73}}{6} \\ \Rightarrow y=\frac{-1+\sqrt{73}}{6} \text { or } y=\frac{-1-\sqrt{73}}{6}\end{array}$

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