a2+18a+26=-9

Solution for a2+18a+26=-9 equation:

a2+18a+26=-9

We move all terms to the left:

a2+18a+26-(-9)=0

We add all the numbers together, and all the variables

a^2+18a+35=0

a = 1; b = 18; c = +35;
Δ = b2-4ac
Δ = 182-4·1·35
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{46}}{2*1}=\frac{-18-2\sqrt{46}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{46}}{2*1}=\frac{-18+2\sqrt{46}}{2}
$