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The given equation is,
[tex]2x^2+3x=2[/tex]Converting to the standard quadratic form, ax² + bx + c = 0, we have,
[tex]2x^2+3x-2=0[/tex]We have the solution for the quadratic equation as,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Here,
[tex]\begin{gathered} a=2 \\ b=3 \\ c=-2 \end{gathered}[/tex]Substituting, we get,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-(4)(2)(-2)}}{2\times2} \\ =\frac{-3\pm\sqrt[]{9+16}}{4} \\ =\frac{-3\pm5}{4} \\ =\frac{-3+5}{4};\frac{-3-5}{4} \\ =\frac{1}{2};-2 \end{gathered}[/tex]