0=5x^2+2x-1

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

0=5x^2+2x-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -5; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-5)·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*-5}=\frac{2-2\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*-5}=\frac{2+2\sqrt{6}}{-10}
$