x=(2-0.01x)x-16

Solution for x=(2-0.01x)x-16 equation:

x=(2-0.01x)x-16

We move all terms to the left:

x-((2-0.01x)x-16)=0

We add all the numbers together, and all the variables

x-((-0.01x+2)x-16)=0


We calculate terms in parentheses: -((-0.01x+2)x-16), so:

(-0.01x+2)x-16

We multiply parentheses

0x^2+2x-16

We add all the numbers together, and all the variables

x^2+2x-16

Back to the equation:

-(x^2+2x-16)


We get rid of parentheses

-x^2+x-2x+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}
$