(-1/5x^2)+4=-1

Solution for (-1/5x^2)+4=-1 equation:

(-1/5x^2)+4=-1

We move all terms to the left:

(-1/5x^2)+4-(-1)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-1/5x^2+5=0

We multiply all the terms by the denominator


5*5x^2-1=0

Wy multiply elements

25x^2-1=0

a = 25; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·25·(-1)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*25}=\frac{-10}{50}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*25}=\frac{10}{50}
=1/5
$