(X)=40x-0.25x^2

Solution for (X)=40x-0.25x^2 equation:

(X)=40X-0.25X^2

We move all terms to the left:

(X)-(40X-0.25X^2)=0

We get rid of parentheses

0.25X^2-40X+X=0

We add all the numbers together, and all the variables

0.25X^2-39X=0

a = 0.25; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·0.25·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*0.25}=\frac{0}{0.5}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*0.25}=\frac{78}{0.5}
=156
$