12x^2+3x+54=180

Solution for 12x^2+3x+54=180 equation:

12x^2+3x+54=180

We move all terms to the left:

12x^2+3x+54-(180)=0

We add all the numbers together, and all the variables

12x^2+3x-126=0

a = 12; b = 3; c = -126;
Δ = b2-4ac
Δ = 32-4·12·(-126)
Δ = 6057
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:

$\sqrt{\Delta}=\sqrt{6057}=\sqrt{9*673}=\sqrt{9}*\sqrt{673}=3\sqrt{673}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{673}}{2*12}=\frac{-3-3\sqrt{673}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{673}}{2*12}=\frac{-3+3\sqrt{673}}{24}
$