R function to solve a quadratic equation - r

I am trying to solve for x of the following quadratic equation:
where
a_i<-c(9,27,37,47)
b_i<-c(70,35,24,6)
a=sum(a_i)
b=sum(b_i)
d_i<-c(1,-1,-1,1)
I am not sure what kind of R function I should use. I tried uniroot but could not solve it. Would anyone guide me on this?

Related

R linprog delivers incorrect solution

I am solving the following simple linear program with pracma::linprog in R:
library(pracma)
cc=c(1)
A=as.matrix(-1)
b=c(1)
linprog(cc,A,b,maximize=FALSE)
The solution returned is x=0.
However, this solution is incorrect: a lower value of the linear program can clearly be obtained at x=-1.
I find that both Wolfram Alpha and Matlab return the correct solution.
Why does linprog return the wrong solution? Is there any way to correct this problem?

From ?linprog
This is a first version that will be unstable at times. For real
linear programming problems use package lpSolve
Which gives the same answer
lpSolve::lp(direction='min', cc,A,"<=",b)
Success: the objective function is 0
And from ?lp
Note that every variable is assumed to be >= 0!

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Find the x value based on a regression inverse function in R

I was seeking for solutions to inverse functions in R. The uniroot() indicates a possible to do this, however I don't know how.
My problem is quite simple, I guess. I have a nonlinear regression as trigonometric function:
function(d,x) d*sqrt(-0.9298239*(x-1)+0.0351246*sin(2.0737115*pi*x)+0.0037540*(1/tan(pi*x/2)))
I need to find the x value based on y value. How can I do that?
Edit: If I plot the curve using the expression (f(x)-y) I have something like the image below. Now, how could I extract the value that minimizes in zero?
minimization

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