-4w^2-13w-3=0

Solution for -4w^2-13w-3=0 equation:

-4w^2-13w-3=0

a = -4; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·(-4)·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*-4}=\frac{2}{-8}
=-1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*-4}=\frac{24}{-8}
=-3
$