g2+14g=37

Solution for g2+14g=37 equation:

g2+14g=37

We move all terms to the left:

g2+14g-(37)=0

We add all the numbers together, and all the variables

g^2+14g-37=0

a = 1; b = 14; c = -37;
Δ = b2-4ac
Δ = 142-4·1·(-37)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{86}}{2*1}=\frac{-14-2\sqrt{86}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{86}}{2*1}=\frac{-14+2\sqrt{86}}{2}
$