4w^2-27w-6=0

Solution for 4w^2-27w-6=0 equation:

4w^2-27w-6=0

a = 4; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·4·(-6)
Δ = 825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-5\sqrt{33}}{2*4}=\frac{27-5\sqrt{33}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+5\sqrt{33}}{2*4}=\frac{27+5\sqrt{33}}{8}
$