4/5x^2-200=0

Solution for 4/5x^2-200=0 equation:

4/5x^2-200=0


Domain of the equation: 5x^2!=0

x^2!=0/5

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-200*5x^2+4=0

Wy multiply elements

-1000x^2+4=0

a = -1000; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-1000)·4
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*-1000}=\frac{0-40\sqrt{10}}{-2000}
=-\frac{40\sqrt{10}}{-2000}
=-\frac{\sqrt{10}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*-1000}=\frac{0+40\sqrt{10}}{-2000}
=\frac{40\sqrt{10}}{-2000}
=\frac{\sqrt{10}}{-50}
$