20v^2-240v-100=0

Solution for 20v^2-240v-100=0 equation:

20v^2-240v-100=0

a = 20; b = -240; c = -100;
Δ = b2-4ac
Δ = -2402-4·20·(-100)
Δ = 65600
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:

$\sqrt{\Delta}=\sqrt{65600}=\sqrt{1600*41}=\sqrt{1600}*\sqrt{41}=40\sqrt{41}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-40\sqrt{41}}{2*20}=\frac{240-40\sqrt{41}}{40}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+40\sqrt{41}}{2*20}=\frac{240+40\sqrt{41}}{40}
$