x^2-41x^2=-400

Solution for x^2-41x^2=-400 equation:

x^2-41x^2=-400

We move all terms to the left:

x^2-41x^2-(-400)=0

We add all the numbers together, and all the variables

-40x^2+400=0

a = -40; b = 0; c = +400;
Δ = b2-4ac
Δ = 02-4·(-40)·400
Δ = 64000
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:

$\sqrt{\Delta}=\sqrt{64000}=\sqrt{6400*10}=\sqrt{6400}*\sqrt{10}=80\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{10}}{2*-40}=\frac{0-80\sqrt{10}}{-80}
=-\frac{80\sqrt{10}}{-80}
=-\frac{\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{10}}{2*-40}=\frac{0+80\sqrt{10}}{-80}
=\frac{80\sqrt{10}}{-80}
=\frac{\sqrt{10}}{-1}
$