X=(40x+300)-(80x-0.5x^2)

Solution for X=(40x+300)-(80x-0.5x^2) equation:

X=(40X+300)-(80X-0.5X^2)

We move all terms to the left:

X-((40X+300)-(80X-0.5X^2))=0


We calculate terms in parentheses: -((40X+300)-(80X-0.5X^2)), so:

(40X+300)-(80X-0.5X^2)

determiningTheFunctionDomain
-(80X-0.5X^2)+(40X+300)

We get rid of parentheses

0.5X^2-80X+40X+300

We add all the numbers together, and all the variables

0.5X^2-40X+300

Back to the equation:

-(0.5X^2-40X+300)


We add all the numbers together, and all the variables

X-(0.5X^2-40X+300)=0

We get rid of parentheses

-0.5X^2+X+40X-300=0

We add all the numbers together, and all the variables

-0.5X^2+41X-300=0

a = -0.5; b = 41; c = -300;
Δ = b2-4ac
Δ = 412-4·(-0.5)·(-300)
Δ = 1081
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{-(41)-\sqrt{1081}}{2*-0.5}=\frac{-41-\sqrt{1081}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1081}}{2*-0.5}=\frac{-41+\sqrt{1081}}{-1}
$