Y=x*x+x-1

Solution for Y=x*x+x-1 equation:

=Y*Y+Y-1

We move all terms to the left:

-(Y*Y+Y-1)=0

We add all the numbers together, and all the variables

-(Y+Y*Y-1)=0

We get rid of parentheses

-Y-Y*Y+1=0

We add all the numbers together, and all the variables

-1Y-Y*Y+1=0

Wy multiply elements

-1Y^2-1Y+1=0

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

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