(X-2)(x-4)2=100

Solution for (X-2)(x-4)2=100 equation:

(X-2)(X-4)2=100

We move all terms to the left:

(X-2)(X-4)2-(100)=0

We multiply parentheses ..

(+X^2-4X-2X+8)2-100=0

We multiply parentheses

2X^2-8X-4X+16-100=0

We add all the numbers together, and all the variables

2X^2-12X-84=0

a = 2; b = -12; c = -84;
Δ = b2-4ac
Δ = -122-4·2·(-84)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{51}}{2*2}=\frac{12-4\sqrt{51}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{51}}{2*2}=\frac{12+4\sqrt{51}}{4}
$