x^2+27x-9=0

Solution for x^2+27x-9=0 equation:

x^2+27x-9=0

a = 1; b = 27; c = -9;
Δ = b2-4ac
Δ = 272-4·1·(-9)
Δ = 765
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{85}}{2*1}=\frac{-27-3\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{85}}{2*1}=\frac{-27+3\sqrt{85}}{2}
$