4x^2+12x+9=54

Solution for 4x^2+12x+9=54 equation:

4x^2+12x+9=54

We move all terms to the left:

4x^2+12x+9-(54)=0

We add all the numbers together, and all the variables

4x^2+12x-45=0

a = 4; b = 12; c = -45;
Δ = b2-4ac
Δ = 122-4·4·(-45)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{6}}{2*4}=\frac{-12-12\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{6}}{2*4}=\frac{-12+12\sqrt{6}}{8}
$