2=(3x-6)(3x-14)

Solution for 2=(3x-6)(3x-14) equation:

2=(3x-6)(3x-14)

We move all terms to the left:

2-((3x-6)(3x-14))=0

We multiply parentheses ..

-((+9x^2-42x-18x+84))+2=0


We calculate terms in parentheses: -((+9x^2-42x-18x+84)), so:

(+9x^2-42x-18x+84)

We get rid of parentheses

9x^2-42x-18x+84

We add all the numbers together, and all the variables

9x^2-60x+84

Back to the equation:

-(9x^2-60x+84)


We get rid of parentheses

-9x^2+60x-84+2=0

We add all the numbers together, and all the variables

-9x^2+60x-82=0

a = -9; b = 60; c = -82;
Δ = b2-4ac
Δ = 602-4·(-9)·(-82)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-18\sqrt{2}}{2*-9}=\frac{-60-18\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+18\sqrt{2}}{2*-9}=\frac{-60+18\sqrt{2}}{-18}
$