w^2-3w-27=0

Solution for w^2-3w-27=0 equation:

w^2-3w-27=0

a = 1; b = -3; c = -27;
Δ = b2-4ac
Δ = -32-4·1·(-27)
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{13}}{2*1}=\frac{3-3\sqrt{13}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{13}}{2*1}=\frac{3+3\sqrt{13}}{2}
$