-4v^2-31v-27=0

Solution for -4v^2-31v-27=0 equation:

-4v^2-31v-27=0

a = -4; b = -31; c = -27;
Δ = b2-4ac
Δ = -312-4·(-4)·(-27)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-23}{2*-4}=\frac{8}{-8}
=-1
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+23}{2*-4}=\frac{54}{-8}
=-6+3/4
$