(a+6)(a+6)=49

Solution for (a+6)(a+6)=49 equation:

(a+6)(a+6)=49

We move all terms to the left:

(a+6)(a+6)-(49)=0

We multiply parentheses ..

(+a^2+6a+6a+36)-49=0

We get rid of parentheses

a^2+6a+6a+36-49=0

We add all the numbers together, and all the variables

a^2+12a-13=0

a = 1; b = 12; c = -13;
Δ = b2-4ac
Δ = 122-4·1·(-13)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-14}{2*1}=\frac{-26}{2}
=-13
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+14}{2*1}=\frac{2}{2}
=1
$