12x^2-x-6=420

Solution for 12x^2-x-6=420 equation:

12x^2-x-6=420

We move all terms to the left:

12x^2-x-6-(420)=0

We add all the numbers together, and all the variables

12x^2-1x-426=0

a = 12; b = -1; c = -426;
Δ = b2-4ac
Δ = -12-4·12·(-426)
Δ = 20449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20449}=143$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-143}{2*12}=\frac{-142}{24}
=-5+11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+143}{2*12}=\frac{144}{24}
=6
$