2n^2+2n+1=154

Solution for 2n^2+2n+1=154 equation:

2n^2+2n+1=154

We move all terms to the left:

2n^2+2n+1-(154)=0

We add all the numbers together, and all the variables

2n^2+2n-153=0

a = 2; b = 2; c = -153;
Δ = b2-4ac
Δ = 22-4·2·(-153)
Δ = 1228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1228}=\sqrt{4*307}=\sqrt{4}*\sqrt{307}=2\sqrt{307}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{307}}{2*2}=\frac{-2-2\sqrt{307}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{307}}{2*2}=\frac{-2+2\sqrt{307}}{4}
$