(2x-4)(3x-4)=114

Solution for (2x-4)(3x-4)=114 equation:

(2x-4)(3x-4)=114

We move all terms to the left:

(2x-4)(3x-4)-(114)=0

We multiply parentheses ..

(+6x^2-8x-12x+16)-114=0

We get rid of parentheses

6x^2-8x-12x+16-114=0

We add all the numbers together, and all the variables

6x^2-20x-98=0

a = 6; b = -20; c = -98;
Δ = b2-4ac
Δ = -202-4·6·(-98)
Δ = 2752
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:

$\sqrt{\Delta}=\sqrt{2752}=\sqrt{64*43}=\sqrt{64}*\sqrt{43}=8\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{43}}{2*6}=\frac{20-8\sqrt{43}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{43}}{2*6}=\frac{20+8\sqrt{43}}{12}
$