(6x-6)(7x-4)=38

Solution for (6x-6)(7x-4)=38 equation:

(6x-6)(7x-4)=38

We move all terms to the left:

(6x-6)(7x-4)-(38)=0

We multiply parentheses ..

(+42x^2-24x-42x+24)-38=0

We get rid of parentheses

42x^2-24x-42x+24-38=0

We add all the numbers together, and all the variables

42x^2-66x-14=0

a = 42; b = -66; c = -14;
Δ = b2-4ac
Δ = -662-4·42·(-14)
Δ = 6708
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:

$\sqrt{\Delta}=\sqrt{6708}=\sqrt{4*1677}=\sqrt{4}*\sqrt{1677}=2\sqrt{1677}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1677}}{2*42}=\frac{66-2\sqrt{1677}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1677}}{2*42}=\frac{66+2\sqrt{1677}}{84}
$