e+7=e(2)+1

Solution for e+7=e(2)+1 equation:

e+7=e(2)+1

We move all terms to the left:

e+7-(e(2)+1)=0

We add all the numbers together, and all the variables

-(+e^2+1)+e+7=0

We get rid of parentheses

-e^2+e-1+7=0

We add all the numbers together, and all the variables

-1e^2+e+6=0

a = -1; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-1)·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-1}=\frac{-6}{-2}
=+3
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-1}=\frac{4}{-2}
=-2
$