Quadratic formula for 2x² + 3x − 2 = 0

Here are the steps. First, match the equation to the standard form $a{x}^2+bx+c=0$: $a=2$, $b=3$, $c=-2$. Next, substitute into the formula: $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$ Then compute the discriminant, $b^2-4ac$: $3^2-4(2)(-2)=9+16=25$. Because it's positive, there are two real roots. Now finish the formula: $$x=\frac{-3\pm \sqrt{25}}{4}=\frac{-3\pm 5}{4}$$ For the plus sign, $x=\frac{2}{4}=\frac{1}{2}$. For the minus sign, $x=\frac{-8}{4}=-2$. To check, put $x=\frac{1}{2}$ back in: $2(\frac{1}{4})+3(\frac{1}{2})-2=0$. For $x=-2$: $2(4)+3(-2)-2=0$. Both work, so the solutions are $x=\frac{1}{2}$ and $x=-2$.