R(x)=x(110-4x)

Solution for R(x)=x(110-4x) equation:

(R)=R(110-4R)

We move all terms to the left:

(R)-(R(110-4R))=0

We add all the numbers together, and all the variables

R-(R(-4R+110))=0


We calculate terms in parentheses: -(R(-4R+110)), so:

R(-4R+110)

We multiply parentheses

-4R^2+110R

Back to the equation:

-(-4R^2+110R)


We get rid of parentheses

4R^2-110R+R=0

We add all the numbers together, and all the variables

4R^2-109R=0

a = 4; b = -109; c = 0;
Δ = b2-4ac
Δ = -1092-4·4·0
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-109}{2*4}=\frac{0}{8}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+109}{2*4}=\frac{218}{8}
=27+1/4
$