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

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Answer 1 · 2016-03-23T16:52:33

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

$x = color(blue)( 7/8$

$8x^2+42=55x$

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

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:

$Delta=b^2-4*a*c$

$= (-55)^2-(4* 8 * 42)$

$= 3025 - 1344 = 1681$

The solutions are found using the formula:

$x=(-b+-sqrtDelta)/(2*a)$

$x = (-(-55)+-sqrt(1681))/(2*8) = (55+-41)/16$

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

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

How do you solve 8x^2+ 42=55x8x^2+ 42=55x?