9x^2+6x-27=0

Solution for 9x^2+6x-27=0 equation:

9x^2+6x-27=0

a = 9; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·9·(-27)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12\sqrt{7}}{2*9}=\frac{-6-12\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12\sqrt{7}}{2*9}=\frac{-6+12\sqrt{7}}{18}
$