Y=x2+3x+1

Solution for Y=x2+3x+1 equation:

=Y2+3Y+1

We move all terms to the left:

-(Y2+3Y+1)=0

We add all the numbers together, and all the variables

-(+Y^2+3Y+1)=0

We get rid of parentheses

-Y^2-3Y-1=0

We add all the numbers together, and all the variables

-1Y^2-3Y-1=0

a = -1; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·(-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{-(-3)-\sqrt{5}}{2*-1}=\frac{3-\sqrt{5}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5}}{2*-1}=\frac{3+\sqrt{5}}{-2}
$