6294.75=(x*5)+((8.5*(5x-9))+((1/3)*(5x-9)+x))

Solution for 6294.75=(x*5)+((8.5*(5x-9))+((1/3)*(5x-9)+x)) equation:

6294.75=(x*5)+((8.5(5x-9))+((1/3)(5x-9)+x))

We move all terms to the left:

6294.75-((x*5)+((8.5(5x-9))+((1/3)(5x-9)+x)))=0


Domain of the equation: 3)(5x-9)+x)))!=0

x∈R


We add all the numbers together, and all the variables

-((+x*5)+((8.5(5x-9))+((+1/3)(5x-9)+x)))+6294.75=0

We multiply parentheses ..

-((+x*5)+((8.5(5x-9))+((+5x^2+1/3*-9)+x)))+6294.75=0

We multiply all the terms by the denominator


-((+x*5)+((8.5(5x-9))+((+5x^2+1+(6294.75)*3*-9)+x)))=0


We calculate terms in parentheses: -((+x*5)+((8.5(5x-9))+((+5x^2+1+(6294.75)*3*-9)+x))), so:

(+x*5)+((8.5(5x-9))+((+5x^2+1+(6294.75)*3*-9)+x))

determiningTheFunctionDomain
((8.5(5x-9))+((+5x^2+1+(6294.75)*3*-9)+x))+(+x*5)

We get rid of parentheses

((8.5(5x-9))+((+5x^2+1+(6294.75)*3*-9)+x))+x*5


We calculate terms in parentheses: +((8.5(5x-9))+((+5x^2+1+(6294.75)*3*-9)+x)), so:

(8.5(5x-9))+((+5x^2+1+(6294.75)*3*-9)+x)

determiningTheFunctionDomain
((+5x^2+1+(6294.75)*3*-9)+x)+(8.5(5x-9))


We calculate terms in parentheses: +((+5x^2+1+(6294.75)*3*-9)+x), so:

(+5x^2+1+(6294.75)*3*-9)+x


We calculate terms in parentheses: +(+5x^2+1+(6294.75)*3*-9), so:

+5x^2+1+(6294.75)*3*-9

determiningTheFunctionDomain
5x^2+1-9+(6294.75)*3*

We add all the numbers together, and all the variables

5x^2

Back to the equation:

+(5x^2)


Back to the equation:

+(5x^2+x)



We calculate terms in parentheses: +(8.5(5x-9)), so:

8.5(5x-9)

We multiply parentheses

42.5x-76.5

Back to the equation:

+(42.5x-76.5)


We get rid of parentheses

5x^2+x+42.5x-76.5

We add all the numbers together, and all the variables

5x^2+43.5x-76.5

Back to the equation:

+(5x^2+43.5x-76.5)


Wy multiply elements

(5x^2+43.5x-76.5)+5x

We get rid of parentheses

5x^2+43.5x+5x-76.5

We add all the numbers together, and all the variables

5x^2+48.5x-76.5

Back to the equation:

-(5x^2+48.5x-76.5)


We get rid of parentheses

-5x^2-48.5x+76.5=0

a = -5; b = -48.5; c = +76.5;
Δ = b2-4ac
Δ = -48.52-4·(-5)·76.5
Δ = 3882.25
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{-(-48.5)-\sqrt{3882.25}}{2*-5}=\frac{48.5-\sqrt{3882.25}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48.5)+\sqrt{3882.25}}{2*-5}=\frac{48.5+\sqrt{3882.25}}{-10}
$