6v2-12v-58=0

Solution for 6v2-12v-58=0 equation:

6v^2-12v-58=0

a = 6; b = -12; c = -58;
Δ = b2-4ac
Δ = -122-4·6·(-58)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16\sqrt{6}}{2*6}=\frac{12-16\sqrt{6}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16\sqrt{6}}{2*6}=\frac{12+16\sqrt{6}}{12}
$