16=4(u-4)8u

Solution for 16=4(u-4)8u equation:

16=4(u-4)8u

We move all terms to the left:

16-(4(u-4)8u)=0


We calculate terms in parentheses: -(4(u-4)8u), so:

4(u-4)8u

We multiply parentheses

32u^2-128u

Back to the equation:

-(32u^2-128u)


We get rid of parentheses

-32u^2+128u+16=0

a = -32; b = 128; c = +16;
Δ = b2-4ac
Δ = 1282-4·(-32)·16
Δ = 18432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18432}=\sqrt{9216*2}=\sqrt{9216}*\sqrt{2}=96\sqrt{2}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-96\sqrt{2}}{2*-32}=\frac{-128-96\sqrt{2}}{-64}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+96\sqrt{2}}{2*-32}=\frac{-128+96\sqrt{2}}{-64}
$