400+4x^2-80x^2=64x^2

Solution for 400+4x^2-80x^2=64x^2 equation:

400+4x^2-80x^2=64x^2

We move all terms to the left:

400+4x^2-80x^2-(64x^2)=0

We add all the numbers together, and all the variables

-140x^2+400=0

a = -140; b = 0; c = +400;
Δ = b2-4ac
Δ = 02-4·(-140)·400
Δ = 224000
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:

$\sqrt{\Delta}=\sqrt{224000}=\sqrt{6400*35}=\sqrt{6400}*\sqrt{35}=80\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{35}}{2*-140}=\frac{0-80\sqrt{35}}{-280}
=-\frac{80\sqrt{35}}{-280}
=-\frac{2\sqrt{35}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{35}}{2*-140}=\frac{0+80\sqrt{35}}{-280}
=\frac{80\sqrt{35}}{-280}
=\frac{2\sqrt{35}}{-7}
$