5v^2-42v-100=0

Solution for 5v^2-42v-100=0 equation:

5v^2-42v-100=0

a = 5; b = -42; c = -100;
Δ = b2-4ac
Δ = -422-4·5·(-100)
Δ = 3764
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:

$\sqrt{\Delta}=\sqrt{3764}=\sqrt{4*941}=\sqrt{4}*\sqrt{941}=2\sqrt{941}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{941}}{2*5}=\frac{42-2\sqrt{941}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{941}}{2*5}=\frac{42+2\sqrt{941}}{10}
$