X=2x(90-x)

Solution for X=2x(90-x) equation:

X=2X(90-X)

We move all terms to the left:

X-(2X(90-X))=0

We add all the numbers together, and all the variables

X-(2X(-1X+90))=0


We calculate terms in parentheses: -(2X(-1X+90)), so:

2X(-1X+90)

We multiply parentheses

-2X^2+180X

Back to the equation:

-(-2X^2+180X)


We get rid of parentheses

2X^2-180X+X=0

We add all the numbers together, and all the variables

2X^2-179X=0

a = 2; b = -179; c = 0;
Δ = b2-4ac
Δ = -1792-4·2·0
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-179)-179}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+179}{2*2}=\frac{358}{4}
=89+1/2
$