16=0.5(x+4)*(x)

Solution for 16=0.5(x+4)*(x) equation:

16=0.5(x+4)(x)

We move all terms to the left:

16-(0.5(x+4)(x))=0


We calculate terms in parentheses: -(0.5(x+4)x), so:

0.5(x+4)x

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x+16=0

We add all the numbers together, and all the variables

-1x^2-1x+16=0

a = -1; b = -1; c = +16;
Δ = b2-4ac
Δ = -12-4·(-1)·16
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{65}}{2*-1}=\frac{1-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{65}}{2*-1}=\frac{1+\sqrt{65}}{-2}
$