a^2+18a+49=-7

Solution for a^2+18a+49=-7 equation:

a^2+18a+49=-7

We move all terms to the left:

a^2+18a+49-(-7)=0

We add all the numbers together, and all the variables

a^2+18a+56=0

a = 1; b = 18; c = +56;
Δ = b2-4ac
Δ = 182-4·1·56
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10}{2*1}=\frac{-28}{2}
=-14
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10}{2*1}=\frac{-8}{2}
=-4
$