g^2+19g+78=-6

Solution for g^2+19g+78=-6 equation:

g^2+19g+78=-6

We move all terms to the left:

g^2+19g+78-(-6)=0

We add all the numbers together, and all the variables

g^2+19g+84=0

a = 1; b = 19; c = +84;
Δ = b2-4ac
Δ = 192-4·1·84
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-5}{2*1}=\frac{-24}{2}
=-12
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+5}{2*1}=\frac{-14}{2}
=-7
$