100x2+4Y2=400

Solution for 100x2+4Y2=400 equation:

100x^2+42=400

We move all terms to the left:

100x^2+42-(400)=0

We add all the numbers together, and all the variables

100x^2-358=0

a = 100; b = 0; c = -358;
Δ = b2-4ac
Δ = 02-4·100·(-358)
Δ = 143200
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:

$\sqrt{\Delta}=\sqrt{143200}=\sqrt{400*358}=\sqrt{400}*\sqrt{358}=20\sqrt{358}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{358}}{2*100}=\frac{0-20\sqrt{358}}{200}
=-\frac{20\sqrt{358}}{200}
=-\frac{\sqrt{358}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{358}}{2*100}=\frac{0+20\sqrt{358}}{200}
=\frac{20\sqrt{358}}{200}
=\frac{\sqrt{358}}{10}
$