2x^2+2x+1=164

Solution for 2x^2+2x+1=164 equation:

2x^2+2x+1=164

We move all terms to the left:

2x^2+2x+1-(164)=0

We add all the numbers together, and all the variables

2x^2+2x-163=0

a = 2; b = 2; c = -163;
Δ = b2-4ac
Δ = 22-4·2·(-163)
Δ = 1308
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:

$\sqrt{\Delta}=\sqrt{1308}=\sqrt{4*327}=\sqrt{4}*\sqrt{327}=2\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{327}}{2*2}=\frac{-2-2\sqrt{327}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{327}}{2*2}=\frac{-2+2\sqrt{327}}{4}
$