R(X)=-2+5x/x.x.x-x.x-6x

Solution for R(X)=-2+5x/x.x.x-x.x-6x equation:

(R)=-2+5R/R.R.R-R.R-6R

We move all terms to the left:

(R)-(-2+5R/R.R.R-R.R-6R)=0


Domain of the equation: R.R.R-R.R-6R)!=0

R∈R


We add all the numbers together, and all the variables

R-(-6R+5R/R.R.R-R.R-2)=0

We get rid of parentheses

R+6R-5R/R.R.R+R.R+2=0

We multiply all the terms by the denominator


R*R.R.R+6R*R.R.R-5R+(R.R)*R.R.R+2*R.R.R=0

We add all the numbers together, and all the variables

R*R.R.R+6R*R.R.R-5R+(+R.R)*R.R.R+2*R.R.R=0

We add all the numbers together, and all the variables

-5R+R*R.R.R+6R*R.R.R+(+R.R)*R.R.R+2*R.R.R=0

We multiply parentheses

R^2-5R+R*R.R.R+6R*R.R.R+2*R.R.R=0

Wy multiply elements

R^2+R^2+6R^2-5R+2R=0

We add all the numbers together, and all the variables

8R^2-3R=0

a = 8; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·8·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*8}=\frac{0}{16}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*8}=\frac{6}{16}
=3/8
$