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12x^2+162x+384=0
a = 12; b = 162; c = +384;
Δ = b2-4ac
Δ = 1622-4·12·384
Δ = 7812
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7812}=\sqrt{36*217}=\sqrt{36}*\sqrt{217}=6\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-6\sqrt{217}}{2*12}=\frac{-162-6\sqrt{217}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+6\sqrt{217}}{2*12}=\frac{-162+6\sqrt{217}}{24} $
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