400x^2=800

Solution for 400x^2=800 equation:

400x^2=800

We move all terms to the left:

400x^2-(800)=0

a = 400; b = 0; c = -800;
Δ = b2-4ac
Δ = 02-4·400·(-800)
Δ = 1280000
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:

$\sqrt{\Delta}=\sqrt{1280000}=\sqrt{640000*2}=\sqrt{640000}*\sqrt{2}=800\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{2}}{2*400}=\frac{0-800\sqrt{2}}{800}
=-\frac{800\sqrt{2}}{800}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{2}}{2*400}=\frac{0+800\sqrt{2}}{800}
=\frac{800\sqrt{2}}{800}
=\sqrt{2}
$