# How do you solve using the quadratic formula method 4x^2 + 2 = 7x?

May 21, 2016

The solutions for the quadratic equation are:

color(blue)(x =(7+sqrt(17))/8

color(blue)(x =(7-sqrt(17))/8

#### Explanation:

$4 {x}^{2} + 2 = 7 x$

$4 {x}^{2} - 7 x + 2 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 4 , b = - 7 , c = 2$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 7\right)}^{2} - \left(4 \cdot 4 \cdot 2\right)$

$= 49 - 32 = 17$

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(- 7\right) \pm \sqrt{17}}{2 \cdot 4} = \frac{7 \pm \sqrt{17}}{8}$

$x = \frac{7 + \sqrt{17}}{8}$

$x = \frac{7 - \sqrt{17}}{8}$