# I want to solve (x-2*y)^2+3*y = 4 with respect to x (fixed y=k) or y (fixed x=k)
#
# First I look for a "graphic" approximation of the solutions:
f <- function(x,y) (x-2*y)^2+3*y - 4
Plane(-3,4,-4,3)
CURVE(f,"brown")

# Then I proceed by solving the equations numerically, first estimating from the
# graph some intervals for x, or for y, where f(x,k), or f(k,y), changes the sign:
# (I remember that solution(F,7, 1,3) solves F(x)=7 if between 1 and 3 F step across the value 7)
# For which x f(x,y) passes through y=0 to the left of the y axis?
h <- function(x) f(x,0); solution(h,0, -3,-1)
# -2
# For which x passes through y=1 near the y axis?
h <- function(x) f(x,1); ; solution(h,0, 0,2)
# 1
# For which y passes through x=0 under the x axis?
h <- function(y) f(0,y); solution(h,0, -2,-1)
# -1.443
#
# Finally, I check the solutions graphically:
POINT(0,-1.443,"blue"); POINT(1,1,"red"); POINT(-2,0,"black")