4v^2-9.6v-5.76=0

Solution for 4v^2-9.6v-5.76=0 equation:

4v^2-9.6v-5.76=0

a = 4; b = -9.6; c = -5.76;
Δ = b2-4ac
Δ = -9.62-4·4·(-5.76)
Δ = 184.32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9.6)-\sqrt{184.32}}{2*4}=\frac{9.6-\sqrt{184.32}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.6)+\sqrt{184.32}}{2*4}=\frac{9.6+\sqrt{184.32}}{8}
$