4/5*x^2-2=0

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

4/5x^2-2=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


-2*5x^2+4=0

Wy multiply elements

-10x^2+4=0

a = -10; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-10)·4
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-10}=\frac{0-4\sqrt{10}}{-20}
=-\frac{4\sqrt{10}}{-20}
=-\frac{\sqrt{10}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-10}=\frac{0+4\sqrt{10}}{-20}
=\frac{4\sqrt{10}}{-20}
=\frac{\sqrt{10}}{-5}
$