-7v^2-51v-40=0

Solution for -7v^2-51v-40=0 equation:

-7v^2-51v-40=0

a = -7; b = -51; c = -40;
Δ = b2-4ac
Δ = -512-4·(-7)·(-40)
Δ = 1481
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{-(-51)-\sqrt{1481}}{2*-7}=\frac{51-\sqrt{1481}}{-14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{1481}}{2*-7}=\frac{51+\sqrt{1481}}{-14}
$