X2-400=40x

Solution for X2-400=40x equation:

X2-400=40X

We move all terms to the left:

X2-400-(40X)=0

We add all the numbers together, and all the variables

X^2-40X-400=0

a = 1; b = -40; c = -400;
Δ = b2-4ac
Δ = -402-4·1·(-400)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{2}}{2*1}=\frac{40-40\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{2}}{2*1}=\frac{40+40\sqrt{2}}{2}
$