a2+2a+1=a+5

Solution for a2+2a+1=a+5 equation:

a2+2a+1=a+5

We move all terms to the left:

a2+2a+1-(a+5)=0

We add all the numbers together, and all the variables

a^2+2a-(a+5)+1=0

We get rid of parentheses

a^2+2a-a-5+1=0

We add all the numbers together, and all the variables

a^2+a-4=0

a = 1; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·1·(-4)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{17}}{2*1}=\frac{-1-\sqrt{17}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*1}=\frac{-1+\sqrt{17}}{2}
$