9v^2-3v-23=0

Solution for 9v^2-3v-23=0 equation:

9v^2-3v-23=0

a = 9; b = -3; c = -23;
Δ = b2-4ac
Δ = -32-4·9·(-23)
Δ = 837
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{93}}{2*9}=\frac{3-3\sqrt{93}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{93}}{2*9}=\frac{3+3\sqrt{93}}{18}
$