6x^2+3x-27=0

Solution for 6x^2+3x-27=0 equation:

6x^2+3x-27=0

a = 6; b = 3; c = -27;
Δ = b2-4ac
Δ = 32-4·6·(-27)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{73}}{2*6}=\frac{-3-3\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{73}}{2*6}=\frac{-3+3\sqrt{73}}{12}
$