16500=x(26-0.01x)

Solution for 16500=x(26-0.01x) equation:

16500=x(26-0.01x)

We move all terms to the left:

16500-(x(26-0.01x))=0

We add all the numbers together, and all the variables

-(x(-0.01x+26))+16500=0


We calculate terms in parentheses: -(x(-0.01x+26)), so:

x(-0.01x+26)

We multiply parentheses

0x^2+26x

We add all the numbers together, and all the variables

x^2+26x

Back to the equation:

-(x^2+26x)


We get rid of parentheses

-x^2-26x+16500=0

We add all the numbers together, and all the variables

-1x^2-26x+16500=0

a = -1; b = -26; c = +16500;
Δ = b2-4ac
Δ = -262-4·(-1)·16500
Δ = 66676
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:

$\sqrt{\Delta}=\sqrt{66676}=\sqrt{4*16669}=\sqrt{4}*\sqrt{16669}=2\sqrt{16669}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{16669}}{2*-1}=\frac{26-2\sqrt{16669}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{16669}}{2*-1}=\frac{26+2\sqrt{16669}}{-2}
$