12w^2-w-6=0

Solution for 12w^2-w-6=0 equation:

12w^2-w-6=0

We add all the numbers together, and all the variables

12w^2-1w-6=0

a = 12; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·12·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*12}=\frac{-16}{24}
=-2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*12}=\frac{18}{24}
=3/4
$