3(12x^2-7x+1)=0

Solution for 3(12x^2-7x+1)=0 equation:

3(12x^2-7x+1)=0

We multiply parentheses

36x^2-21x+3=0

a = 36; b = -21; c = +3;
Δ = b2-4ac
Δ = -212-4·36·3
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*36}=\frac{18}{72}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*36}=\frac{24}{72}
=1/3
$