1/5x^2+2=3/5x^2

Solution for 1/5x^2+2=3/5x^2 equation:

1/5x^2+2=3/5x^2

We move all terms to the left:

1/5x^2+2-(3/5x^2)=0


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

x^2!=0/5

x^2!=√0

x!=0

x∈R



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

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/5x^2-3/5x^2+2=0

We multiply all the terms by the denominator


2*5x^2+1-3=0

We add all the numbers together, and all the variables

2*5x^2-2=0

Wy multiply elements

10x^2-2=0

a = 10; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·10·(-2)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*10}=\frac{0-4\sqrt{5}}{20}
=-\frac{4\sqrt{5}}{20}
=-\frac{\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*10}=\frac{0+4\sqrt{5}}{20}
=\frac{4\sqrt{5}}{20}
=\frac{\sqrt{5}}{5}
$