x2+18x+54=4x+9

Solution for x2+18x+54=4x+9 equation:

x2+18x+54=4x+9

We move all terms to the left:

x2+18x+54-(4x+9)=0

We add all the numbers together, and all the variables

x^2+18x-(4x+9)+54=0

We get rid of parentheses

x^2+18x-4x-9+54=0

We add all the numbers together, and all the variables

x^2+14x+45=0

a = 1; b = 14; c = +45;
Δ = b2-4ac
Δ = 142-4·1·45
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4}{2*1}=\frac{-10}{2}
=-5
$