R=x(30-0.4x)

Solution for R=x(30-0.4x) equation:

=R(30-0.4R)

We move all terms to the left:

-(R(30-0.4R))=0

We add all the numbers together, and all the variables

-(R(-0.4R+30))=0


We calculate terms in parentheses: -(R(-0.4R+30)), so:

R(-0.4R+30)

We multiply parentheses

0R^2+30R

We add all the numbers together, and all the variables

R^2+30R

Back to the equation:

-(R^2+30R)


We get rid of parentheses

-R^2-30R=0

We add all the numbers together, and all the variables

-1R^2-30R=0

a = -1; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-1)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-1}=\frac{0}{-2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-1}=\frac{60}{-2}
=-30
$