# How do you solve  3x^2 +6 =11x?

May 4, 2016

The solutions are:

$x = 3 , x = \frac{2}{3}$

#### Explanation:

$3 {x}^{2} + 6 = 11 x$

$3 {x}^{2} - 11 x + 6 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 3 , b = - 11 , c = 6$

The Discriminant is given by:

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

$= {\left(- 11\right)}^{2} - \left(4 \cdot 3 \cdot 6\right)$

$= 121 - 72 = 49$

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

$x = \frac{- \left(- 11\right) \pm \sqrt{49}}{2 \cdot 3} = \frac{\left(11 \pm 7\right)}{6}$

$x = \frac{11 + 7}{6} = \frac{18}{6} = 3$

$x = \frac{11 - 7}{6} = \frac{4}{6} = \frac{2}{3}$