2(x-4)(x)=100

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

2(x-4)(x)=100

We move all terms to the left:

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

We multiply parentheses

2x^2-8x-100=0

a = 2; b = -8; c = -100;
Δ = b2-4ac
Δ = -82-4·2·(-100)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{6}}{2*2}=\frac{8-12\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{6}}{2*2}=\frac{8+12\sqrt{6}}{4}
$