6x^2+24x-54=0

Solution for 6x^2+24x-54=0 equation:

6x^2+24x-54=0

a = 6; b = 24; c = -54;
Δ = b2-4ac
Δ = 242-4·6·(-54)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{13}}{2*6}=\frac{-24-12\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{13}}{2*6}=\frac{-24+12\sqrt{13}}{12}
$