X=6+2x(90-x)

Solution for X=6+2x(90-x) equation:

X=6+2X(90-X)

We move all terms to the left:

X-(6+2X(90-X))=0

We add all the numbers together, and all the variables

X-(6+2X(-1X+90))=0


We calculate terms in parentheses: -(6+2X(-1X+90)), so:

6+2X(-1X+90)

determiningTheFunctionDomain
2X(-1X+90)+6

We multiply parentheses

-2X^2+180X+6

Back to the equation:

-(-2X^2+180X+6)


We get rid of parentheses

2X^2-180X+X-6=0

We add all the numbers together, and all the variables

2X^2-179X-6=0

a = 2; b = -179; c = -6;
Δ = b2-4ac
Δ = -1792-4·2·(-6)
Δ = 32089
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{-(-179)-\sqrt{32089}}{2*2}=\frac{179-\sqrt{32089}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+\sqrt{32089}}{2*2}=\frac{179+\sqrt{32089}}{4}
$