2x^2+2x+1=365

Solution for 2x^2+2x+1=365 equation:

2x^2+2x+1=365

We move all terms to the left:

2x^2+2x+1-(365)=0

We add all the numbers together, and all the variables

2x^2+2x-364=0

a = 2; b = 2; c = -364;
Δ = b2-4ac
Δ = 22-4·2·(-364)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-54}{2*2}=\frac{-56}{4}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+54}{2*2}=\frac{52}{4}
=13
$