18x^2+27x-1944=0

Solution for 18x^2+27x-1944=0 equation:

18x^2+27x-1944=0

a = 18; b = 27; c = -1944;
Δ = b2-4ac
Δ = 272-4·18·(-1944)
Δ = 140697
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:

$\sqrt{\Delta}=\sqrt{140697}=\sqrt{729*193}=\sqrt{729}*\sqrt{193}=27\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27\sqrt{193}}{2*18}=\frac{-27-27\sqrt{193}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27\sqrt{193}}{2*18}=\frac{-27+27\sqrt{193}}{36}
$