16=x(2x-4)6

Solution for 16=x(2x-4)6 equation:

16=x(2x-4)6

We move all terms to the left:

16-(x(2x-4)6)=0


We calculate terms in parentheses: -(x(2x-4)6), so:

x(2x-4)6

We multiply parentheses

12x^2-24x

Back to the equation:

-(12x^2-24x)


We get rid of parentheses

-12x^2+24x+16=0

a = -12; b = 24; c = +16;
Δ = b2-4ac
Δ = 242-4·(-12)·16
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{21}}{2*-12}=\frac{-24-8\sqrt{21}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{21}}{2*-12}=\frac{-24+8\sqrt{21}}{-24}
$