54.6=4x*x/(0.0056-0.15x+(x*x))

Solution for 54.6=4x*x/(0.0056-0.15x+(x*x)) equation:

54.6=4x*x/(0.0056-0.15x+(x*x))

We move all terms to the left:

54.6-(4x*x/(0.0056-0.15x+(x*x)))=0


Domain of the equation: (0.0056-0.15x+(x*x)))!=0

We move all terms containing x to the left, all other terms to the right

-0.15x+(x*x))!=-0.0056

x∈R


We add all the numbers together, and all the variables

-(4x*x/(0.0056-0.15x+(+x*x)))+54.6=0

We multiply all the terms by the denominator


-(4x*x+(54.6)*(0.0056-0.15x+(+x*x)))=0


We calculate terms in parentheses: -(4x*x+(54.6)*(0.0056-0.15x+(+x*x))), so:

4x*x+(54.6)*(0.0056-0.15x+(+x*x))

Wy multiply elements

4x^2+(54.6)*(0.0056-0.15x+(+x*x))


We calculate terms in parentheses: +(54.6)*(0.0056-0.15x+(+x*x)), so:

54.6)*(0.0056-0.15x+(+x*x)

determiningTheFunctionDomain
-0.15x+(+x*x)+54.6)*(0.0056

We add all the numbers together, and all the variables

-0.15x+(+x*x)

We get rid of parentheses

-0.15x+x*x

Wy multiply elements

x^2-0.15x

Back to the equation:

+(x^2-0.15x)


We get rid of parentheses

4x^2+x^2-0.15x

We add all the numbers together, and all the variables

5x^2-0.15x

Back to the equation:

-(5x^2-0.15x)


We get rid of parentheses

-5x^2+0.15x=0

a = -5; b = 0.15; c = 0;
Δ = b2-4ac
Δ = 0.152-4·(-5)·0
Δ = 0.0225
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{-(0.15)-\sqrt{0.0225}}{2*-5}=\frac{-0.15-\sqrt{0.0225}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.15)+\sqrt{0.0225}}{2*-5}=\frac{-0.15+\sqrt{0.0225}}{-10}
$