5v^2-19v-22=0

Solution for 5v^2-19v-22=0 equation:

5v^2-19v-22=0

a = 5; b = -19; c = -22;
Δ = b2-4ac
Δ = -192-4·5·(-22)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{89}}{2*5}=\frac{19-3\sqrt{89}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{89}}{2*5}=\frac{19+3\sqrt{89}}{10}
$