# How do you find the solution to the quadratic equation 2x^2 + 7 = 3x?

Jun 18, 2018

color(maroon)(x_+ = (3 + i sqrt(47)) / 4, x_- = (3 - i sqrt(47))/4

#### Explanation:

$2 {x}^{2} + 7 = 3 x$

$2 {x}^{2} - 3 x + 7 = 0$

$a = 2 , b = - 3 , c = 7$

$x = \frac{- \left(- 3\right) \pm \sqrt{{\left(- 3\right)}^{2} - \left(4 \cdot 2 \cdot 7\right)}}{2 \cdot 2}$

$x = \frac{3 \pm \sqrt{9 - 56}}{4}$

$x = \frac{3 \pm \sqrt{- 47}}{4}$

color(maroon)(x_+ = (3 + i sqrt(47)) / 4, x_- = (3 - i sqrt(47))/4