R(X)=X^2-40x

Solution for R(X)=X^2-40x equation:

(R)=R^2-40R

We move all terms to the left:

(R)-(R^2-40R)=0

We get rid of parentheses

-R^2+R+40R=0

We add all the numbers together, and all the variables

-1R^2+41R=0

a = -1; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-1)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-1}=\frac{-82}{-2}
=+41
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-1}=\frac{0}{-2}
=0
$