# How do you use the quadratic formula to solve 3x^2-2x+7=0?

Our equation is of the form $a {x}^{2} + b x + c = 0$, therefore, we can use the quadratic formula. The quadratic formula is $x = \frac{- b \pm \sqrt{D}}{2 a}$, with $D = {b}^{2} - 4 a c$. We see that $a = 3 , b = - 2$ and $c = 7$.
Firstly, we calculate $D$.
$D = {b}^{2} - 4 a c = {\left(- 2\right)}^{2} - 4 \cdot 3 \cdot 7 = - 80$. Because D is less than zero, there are no real roots. We can however calculate the imaginary solutions. We just calculate $x$:
$x = \frac{- b \pm \sqrt{D}}{2 a} = \frac{2 \pm \sqrt{- 80}}{2 \cdot 3} = \frac{2 \pm \sqrt{- 1} \cdot \sqrt{16} \cdot \sqrt{5}}{6} = \frac{2 \pm i \cdot 4 \sqrt{5}}{6} = \frac{1}{3} \pm \frac{2}{3} i \sqrt{5}$