X(7x-6)=12

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

X(7X-6)=12

We move all terms to the left:

X(7X-6)-(12)=0

We multiply parentheses

7X^2-6X-12=0

a = 7; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·7·(-12)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{93}}{2*7}=\frac{6-2\sqrt{93}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{93}}{2*7}=\frac{6+2\sqrt{93}}{14}
$