R=(17+x)(74-2x)

Solution for R=(17+x)(74-2x) equation:

=(17+R)(74-2R)

We move all terms to the left:

-((17+R)(74-2R))=0

We add all the numbers together, and all the variables

-((R+17)(-2R+74))=0

We multiply parentheses ..

-((-2R^2+74R-34R+1258))=0


We calculate terms in parentheses: -((-2R^2+74R-34R+1258)), so:

(-2R^2+74R-34R+1258)

We get rid of parentheses

-2R^2+74R-34R+1258

We add all the numbers together, and all the variables

-2R^2+40R+1258

Back to the equation:

-(-2R^2+40R+1258)


We get rid of parentheses

2R^2-40R-1258=0

a = 2; b = -40; c = -1258;
Δ = b2-4ac
Δ = -402-4·2·(-1258)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-108}{2*2}=\frac{-68}{4}
=-17
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+108}{2*2}=\frac{148}{4}
=37
$