R=10x-0.25*(x*x)

Solution for R=10x-0.25*(x*x) equation:

=10R-0.25(R*R)

We move all terms to the left:

-(10R-0.25(R*R))=0

We add all the numbers together, and all the variables

-(10R-0.25(+R*R))=0


We calculate terms in parentheses: -(10R-0.25(+R*R)), so:

10R-0.25(+R*R)

We multiply parentheses

-0.25R^2+10R

Back to the equation:

-(-0.25R^2+10R)


We get rid of parentheses

0.25R^2-10R=0

a = 0.25; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·0.25·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*0.25}=\frac{0}{0.5}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*0.25}=\frac{20}{0.5}
=40
$