12x(7x-6)=41

Solution for 12x(7x-6)=41 equation:

12x(7x-6)=41

We move all terms to the left:

12x(7x-6)-(41)=0

We multiply parentheses

84x^2-72x-41=0

a = 84; b = -72; c = -41;
Δ = b2-4ac
Δ = -722-4·84·(-41)
Δ = 18960
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:

$\sqrt{\Delta}=\sqrt{18960}=\sqrt{16*1185}=\sqrt{16}*\sqrt{1185}=4\sqrt{1185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{1185}}{2*84}=\frac{72-4\sqrt{1185}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{1185}}{2*84}=\frac{72+4\sqrt{1185}}{168}
$