# How do you solve 4x^2=12x-11?

Sep 22, 2015

The solutions are
color(blue)( (12+sqrt(-32))/8

color(blue)( (12-sqrt(-32))/8

#### Explanation:

4x^2=12x−11

$4 {x}^{2} - 12 x + 11 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 4 , b = - 12 , c = 11$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 12\right)}^{2} - \left(4 \cdot 4 \cdot 11\right)$

$= 144 - 176 = - 32$

As $\Delta < 0$ there are no real solutions

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

$x = \frac{- \left(- 12\right) \pm \sqrt{- 32}}{2 \cdot 4} = \frac{12 \pm \sqrt{- 32}}{8}$

The solutions are
color(blue)( (12+sqrt(-32))/8
color(blue)( (12-sqrt(-32))/8