Solve $2x^2+3x-2=0$

Step-by-step solution

1. Step 1 · Discriminant
   $$\Delta =3^2-4(2)(-2)=25$$

   A positive perfect-square discriminant means two rational roots.

2. Step 2 · Quadratic formula
   $$x=\frac{-3\pm \sqrt{25}}{4}$$

   Substitute a = 2, b = 3, c = −2.

3. Step 3 · Evaluate both signs
   $$x=\frac{-3+5}{4}=\frac{1}{2},x=\frac{-3-5}{4}=-2$$

   The ± gives the two roots.