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

Solution for x^2+x/5-1/5=0 equation:

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

We multiply all the terms by the denominator


x^2*5+x-1=0

Wy multiply elements

5x^2+x-1=0

a = 5; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·5·(-1)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{21}}{2*5}=\frac{-1-\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*5}=\frac{-1+\sqrt{21}}{10}
$