18^3-55x^2-28x=0

Solution for 18^3-55x^2-28x=0 equation:

18^3-55x^2-28x=0

We add all the numbers together, and all the variables

-55x^2-28x+5832=0

a = -55; b = -28; c = +5832;
Δ = b2-4ac
Δ = -282-4·(-55)·5832
Δ = 1283824
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:

$\sqrt{\Delta}=\sqrt{1283824}=\sqrt{16*80239}=\sqrt{16}*\sqrt{80239}=4\sqrt{80239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{80239}}{2*-55}=\frac{28-4\sqrt{80239}}{-110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{80239}}{2*-55}=\frac{28+4\sqrt{80239}}{-110}
$