4w^2-23w-6=0

Solution for 4w^2-23w-6=0 equation:

4w^2-23w-6=0

a = 4; b = -23; c = -6;
Δ = b2-4ac
Δ = -232-4·4·(-6)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-25}{2*4}=\frac{-2}{8}
=-1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*4}=\frac{48}{8}
=6
$