2(x-4)(x-4)=338

Solution for 2(x-4)(x-4)=338 equation:

2(x-4)(x-4)=338

We move all terms to the left:

2(x-4)(x-4)-(338)=0

We multiply parentheses ..

2(+x^2-4x-4x+16)-338=0

We multiply parentheses

2x^2-8x-8x+32-338=0

We add all the numbers together, and all the variables

2x^2-16x-306=0

a = 2; b = -16; c = -306;
Δ = b2-4ac
Δ = -162-4·2·(-306)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-52}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+52}{2*2}=\frac{68}{4}
=17
$