7x(3x-4)=12

Solution for 7x(3x-4)=12 equation:

7x(3x-4)=12

We move all terms to the left:

7x(3x-4)-(12)=0

We multiply parentheses

21x^2-28x-12=0

a = 21; b = -28; c = -12;
Δ = b2-4ac
Δ = -282-4·21·(-12)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-16\sqrt{7}}{2*21}=\frac{28-16\sqrt{7}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+16\sqrt{7}}{2*21}=\frac{28+16\sqrt{7}}{42}
$