g^2-22g-17=0

Solution for g^2-22g-17=0 equation:

g^2-22g-17=0

a = 1; b = -22; c = -17;
Δ = b2-4ac
Δ = -222-4·1·(-17)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{138}}{2*1}=\frac{22-2\sqrt{138}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{138}}{2*1}=\frac{22+2\sqrt{138}}{2}
$