28=2x^2+2x+1

Solution for 28=2x^2+2x+1 equation:

28=2x^2+2x+1

We move all terms to the left:

28-(2x^2+2x+1)=0

We get rid of parentheses

-2x^2-2x-1+28=0

We add all the numbers together, and all the variables

-2x^2-2x+27=0

a = -2; b = -2; c = +27;
Δ = b2-4ac
Δ = -22-4·(-2)·27
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{55}}{2*-2}=\frac{2-2\sqrt{55}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{55}}{2*-2}=\frac{2+2\sqrt{55}}{-4}
$