2x^2+27x-9=0

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

2x^2+27x-9=0

a = 2; b = 27; c = -9;
Δ = b2-4ac
Δ = 272-4·2·(-9)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{89}}{2*2}=\frac{-27-3\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{89}}{2*2}=\frac{-27+3\sqrt{89}}{4}
$