R(x)=(340+4x)(75-3x)

Solution for R(x)=(340+4x)(75-3x) equation:

(R)=(340+4R)(75-3R)

We move all terms to the left:

(R)-((340+4R)(75-3R))=0

We add all the numbers together, and all the variables

R-((4R+340)(-3R+75))=0

We multiply parentheses ..

-((-12R^2+300R-1020R+25500))+R=0


We calculate terms in parentheses: -((-12R^2+300R-1020R+25500)), so:

(-12R^2+300R-1020R+25500)

We get rid of parentheses

-12R^2+300R-1020R+25500

We add all the numbers together, and all the variables

-12R^2-720R+25500

Back to the equation:

-(-12R^2-720R+25500)


We get rid of parentheses

12R^2+720R+R-25500=0

We add all the numbers together, and all the variables

12R^2+721R-25500=0

a = 12; b = 721; c = -25500;
Δ = b2-4ac
Δ = 7212-4·12·(-25500)
Δ = 1743841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(721)-\sqrt{1743841}}{2*12}=\frac{-721-\sqrt{1743841}}{24}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(721)+\sqrt{1743841}}{2*12}=\frac{-721+\sqrt{1743841}}{24}
$