# How do you solve 8x^2+ 42=55x?

Mar 23, 2016

The solutions are:
x = color(blue)( 6

x = color(blue)( 7/8

#### Explanation:

$8 {x}^{2} + 42 = 55 x$

$8 {x}^{2} - 55 x + 42 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 8 , b = - 55 , c = 42$

The Discriminant is given by:

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

$= {\left(- 55\right)}^{2} - \left(4 \cdot 8 \cdot 42\right)$

$= 3025 - 1344 = 1681$

The solutions are found using the formula:

$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(- 55\right) \pm \sqrt{1681}}{2 \cdot 8} = \frac{55 \pm 41}{16}$

x = (55+41)/16 = 96/16 = color(blue)( 6

x = (55 - 41)/16 = 14/16 = color(blue)( 7/8