3x^2-12x-54=-3

Solution for 3x^2-12x-54=-3 equation:

3x^2-12x-54=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-12x-51=0

a = 3; b = -12; c = -51;
Δ = b2-4ac
Δ = -122-4·3·(-51)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{21}}{2*3}=\frac{12-6\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{21}}{2*3}=\frac{12+6\sqrt{21}}{6}
$