0. \( 2 x^{2}=5 x+3 \)

To solve the equation \( 2x^{2} = 5x + 3 \), you first need to set it to standard form by moving everything to one side. Rearranging gives \( 2x^{2} - 5x - 3 = 0 \). Now, you can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 2 \), \( b = -5 \), and \( c = -3 \). After inserting the values into the formula, calculate the discriminant \( b^2 - 4ac \) to determine the nature of the roots. Once that's done, plug in the values and solve for \( x \)! To double-check your solutions, substitute the values of \( x \) back into the original equation to ensure both sides are equal. This not only confirms your solutions but also strengthens your understanding of how quadratic equations work!