x=5x^2+2x-1

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

x=5x^2+2x-1

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2-1x+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}
$