g^2-12g-49=0

Solution for g^2-12g-49=0 equation:

g^2-12g-49=0

a = 1; b = -12; c = -49;
Δ = b2-4ac
Δ = -122-4·1·(-49)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{85}}{2*1}=\frac{12-2\sqrt{85}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{85}}{2*1}=\frac{12+2\sqrt{85}}{2}
$