12a2-3a-12=0

Solution for 12a2-3a-12=0 equation:

12a^2-3a-12=0

a = 12; b = -3; c = -12;
Δ = b2-4ac
Δ = -32-4·12·(-12)
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{65}}{2*12}=\frac{3-3\sqrt{65}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{65}}{2*12}=\frac{3+3\sqrt{65}}{24}
$