2x^2+6x+54+18x=0

Solution for 2x^2+6x+54+18x=0 equation:

2x^2+6x+54+18x=0

We add all the numbers together, and all the variables

2x^2+24x+54=0

a = 2; b = 24; c = +54;
Δ = b2-4ac
Δ = 242-4·2·54
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*2}=\frac{-12}{4}
=-3
$