A quadratic solved by the formula

Text

Solve using the quadratic formula: $2x^{2}+3x-4=0.$

Solution

Discriminant: $\Delta=3^{2}-4\cdot 2\cdot(-4)=9+32=41$. $x=\frac{-3\pm\sqrt{41}}{4}.$ Numerically $\sqrt{41}\approx 6.403$, so $x_1\approx 0.851$ and $x_2\approx -2.351$. $\boxed{\,x=\dfrac{-3\pm\sqrt{41}}{4}\,}$