16=-x(90-x)

Solution for 16=-x(90-x) equation:

16=-x(90-x)

We move all terms to the left:

16-(-x(90-x))=0

We add all the numbers together, and all the variables

-(-x(-1x+90))+16=0


We calculate terms in parentheses: -(-x(-1x+90)), so:

-x(-1x+90)

We multiply parentheses

1x^2-90x

We add all the numbers together, and all the variables

x^2-90x

Back to the equation:

-(x^2-90x)


We get rid of parentheses

-x^2+90x+16=0

We add all the numbers together, and all the variables

-1x^2+90x+16=0

a = -1; b = 90; c = +16;
Δ = b2-4ac
Δ = 902-4·(-1)·16
Δ = 8164
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:

$\sqrt{\Delta}=\sqrt{8164}=\sqrt{4*2041}=\sqrt{4}*\sqrt{2041}=2\sqrt{2041}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2041}}{2*-1}=\frac{-90-2\sqrt{2041}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2041}}{2*-1}=\frac{-90+2\sqrt{2041}}{-2}
$