3x^2-6x-54=0

Solution for 3x^2-6x-54=0 equation:

3x^2-6x-54=0

a = 3; b = -6; c = -54;
Δ = b2-4ac
Δ = -62-4·3·(-54)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{19}}{2*3}=\frac{6-6\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{19}}{2*3}=\frac{6+6\sqrt{19}}{6}
$