9g^2-12g-19=0

Solution for 9g^2-12g-19=0 equation:

9g^2-12g-19=0

a = 9; b = -12; c = -19;
Δ = b2-4ac
Δ = -122-4·9·(-19)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{23}}{2*9}=\frac{12-6\sqrt{23}}{18}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{23}}{2*9}=\frac{12+6\sqrt{23}}{18}
$