-18x^2+24x+41=0

Solution for -18x^2+24x+41=0 equation:

-18x^2+24x+41=0

a = -18; b = 24; c = +41;
Δ = b2-4ac
Δ = 242-4·(-18)·41
Δ = 3528
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:

$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-42\sqrt{2}}{2*-18}=\frac{-24-42\sqrt{2}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+42\sqrt{2}}{2*-18}=\frac{-24+42\sqrt{2}}{-36}
$