(X)=40x^2-400x+500

Solution for (X)=40x^2-400x+500 equation:

(X)=40X^2-400X+500

We move all terms to the left:

(X)-(40X^2-400X+500)=0

We get rid of parentheses

-40X^2+X+400X-500=0

We add all the numbers together, and all the variables

-40X^2+401X-500=0

a = -40; b = 401; c = -500;
Δ = b2-4ac
Δ = 4012-4·(-40)·(-500)
Δ = 80801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80801}=\sqrt{49*1649}=\sqrt{49}*\sqrt{1649}=7\sqrt{1649}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(401)-7\sqrt{1649}}{2*-40}=\frac{-401-7\sqrt{1649}}{-80}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(401)+7\sqrt{1649}}{2*-40}=\frac{-401+7\sqrt{1649}}{-80}
$