Given:
#y=(2x-4)(x-1)-5x^2+4x#
FOIL #(2x-4)(x-1)#.
#y=[2x^2-2x-4x+4]-5x^2+4x#
Simplify.
#y=[2x^2-6x+4]-5x^2+4x#
Gather like terms.
#y=(2x^2-5x^2)+(-6x+4x)+4#
Combine like terms.
#y=-3x^2-2x+4# #larr# quadratic equation standard form:
#y=ax^2+bx+c#,
where:
#a=-3#, #b=-2#, and #c=4#.
Quadratic Formula
Substitute #0# for #y#. Solve for #x#.
#0=-3x^2-2x+4#
#x=(-b+-sqrt(b^2-4ac))/(2a)#
Plug in the known values.
#x=(-(-2)+-sqrt((-2)^2-4*-3*4))/(2*-3)#
Simplify.
#x=(2+-sqrt(4+48))/(-6)#
#x=(2+-sqrt52)/(-6)#
Prime factorize #52#.
#x=(2+-sqrt(2xx2xx13))/(-6)#
Simplify.
#(2+-2sqrt13)/(-6)#
Simplify.
#(color(red)cancel(color(black)(2^1))+-(color(red)cancel(color(black)(2^1))sqrt13))/(-(color(red)cancel(color(black)(6^3)))#
#x=(1+-sqrt3)/-3#
Roots
#x=-(1+sqrt13)/3,##-(1-sqrt13)/3#
