# How do you solve 4x^2 – 12x = -9?

Sep 14, 2015

color(blue)(x=3/2

#### Explanation:

4x^2–12x+9=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 4 , b = - 12 , c = 9$

The Discriminant is given by:
color(blue)(Delta=b^2-4*a*c
$= {\left(- 12\right)}^{2} - \left(4 \cdot 4 \cdot 9\right)$
$= 144 - 144 = 0$

As $\Delta = 0$ there is only one solution.

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

$x = \frac{- \left(- 12\right) \pm \sqrt{0}}{2 \cdot 4} = \frac{12 + 0}{8} = \frac{12}{8} = \frac{3}{2}$

The solution is
color(blue)(x=3/2