6g^2=-28-86g

Solution for 6g^2=-28-86g equation:

6g^2=-28-86g

We move all terms to the left:

6g^2-(-28-86g)=0

We add all the numbers together, and all the variables

6g^2-(-86g-28)=0

We get rid of parentheses

6g^2+86g+28=0

a = 6; b = 86; c = +28;
Δ = b2-4ac
Δ = 862-4·6·28
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-82}{2*6}=\frac{-168}{12}
=-14
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+82}{2*6}=\frac{-4}{12}
=-1/3
$