3=6x^2-12x-123

Solution for 3=6x^2-12x-123 equation:

3=6x^2-12x-123

We move all terms to the left:

3-(6x^2-12x-123)=0

We get rid of parentheses

-6x^2+12x+123+3=0

We add all the numbers together, and all the variables

-6x^2+12x+126=0

a = -6; b = 12; c = +126;
Δ = b2-4ac
Δ = 122-4·(-6)·126
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{22}}{2*-6}=\frac{-12-12\sqrt{22}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{22}}{2*-6}=\frac{-12+12\sqrt{22}}{-12}
$