12x(9x-7)=28

Solution for 12x(9x-7)=28 equation:

12x(9x-7)=28

We move all terms to the left:

12x(9x-7)-(28)=0

We multiply parentheses

108x^2-84x-28=0

a = 108; b = -84; c = -28;
Δ = b2-4ac
Δ = -842-4·108·(-28)
Δ = 19152
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:

$\sqrt{\Delta}=\sqrt{19152}=\sqrt{144*133}=\sqrt{144}*\sqrt{133}=12\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{133}}{2*108}=\frac{84-12\sqrt{133}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{133}}{2*108}=\frac{84+12\sqrt{133}}{216}
$