#x^2 - 4x -8 =0 #
The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-4, c= - 8#
The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-4)^2-(4 * 1 * -( 8))#
# = 16 + 32 = 48#
The solutions are found using the formula:
#x=(-b+-sqrtDelta)/(2*a)#
#x = (-(-4)+-sqrt(48))/(2*1) = (4+-sqrt(48))/2#
#sqrt48 = sqrt (2*2*2*2*3)= sqrt ( 2^2 *2 ^2 *3)= 4sqrt3#
#x = (4+-sqrt(48))/2 = (4+-4sqrt(3))/2#
#= ((cancel4 ) * ( 1 +- sqrt3)) /cancel2#
#x= (2) * ( 1 + sqrt3)#
#color(green)(x= 2 + sqrt3#
#x= (2) * ( 1 - sqrt3))#
#color(green)(x= 2 - sqrt3)#
