x=40x^2-400x+1000

Solution for x=40x^2-400x+1000 equation:

x=40x^2-400x+1000

We move all terms to the left:

x-(40x^2-400x+1000)=0

We get rid of parentheses

-40x^2+x+400x-1000=0

We add all the numbers together, and all the variables

-40x^2+401x-1000=0

a = -40; b = 401; c = -1000;
Δ = b2-4ac
Δ = 4012-4·(-40)·(-1000)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(401)-3\sqrt{89}}{2*-40}=\frac{-401-3\sqrt{89}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(401)+3\sqrt{89}}{2*-40}=\frac{-401+3\sqrt{89}}{-80}
$