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
