R(x)=-3(x^2-25x+156.25)+468.75

Solution for R(x)=-3(x^2-25x+156.25)+468.75 equation:

(R)=-3(R^2-25R+156.25)+468.75

We move all terms to the left:

(R)-(-3(R^2-25R+156.25)+468.75)=0


We calculate terms in parentheses: -(-3(R^2-25R+156.25)+468.75), so:

-3(R^2-25R+156.25)+468.75

We multiply parentheses

-3R^2+75R-468.75+468.75

We add all the numbers together, and all the variables

-3R^2+75R

Back to the equation:

-(-3R^2+75R)


We get rid of parentheses

3R^2-75R+R=0

We add all the numbers together, and all the variables

3R^2-74R=0

a = 3; b = -74; c = 0;
Δ = b2-4ac
Δ = -742-4·3·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-74}{2*3}=\frac{0}{6}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+74}{2*3}=\frac{148}{6}
=24+2/3
$