g^2+6g=84

Solution for g^2+6g=84 equation:

g^2+6g=84

We move all terms to the left:

g^2+6g-(84)=0

a = 1; b = 6; c = -84;
Δ = b2-4ac
Δ = 62-4·1·(-84)
Δ = 372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{93}}{2*1}=\frac{-6-2\sqrt{93}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{93}}{2*1}=\frac{-6+2\sqrt{93}}{2}
$