129=(0.417+2x)/(0.0279-x^2)

Solution for 129=(0.417+2x)/(0.0279-x^2) equation:

129=(0.417+2x)/(0.0279-x^2)

We move all terms to the left:

129-((0.417+2x)/(0.0279-x^2))=0


Domain of the equation: (0.0279-x^2))!=0

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

-x^2)!=-0.0279

x!=-0.0279/1

x!=-0.0279

x∈R


We add all the numbers together, and all the variables

-((2x+0.417)/(0.0279-x^2))+129=0

We multiply all the terms by the denominator


-((2x+0.417)+129*(0.0279-x^2))=0


We calculate terms in parentheses: -((2x+0.417)+129*(0.0279-x^2)), so:

(2x+0.417)+129*(0.0279-x^2)

determiningTheFunctionDomain
129*(0.0279-x^2)+(2x+0.417)

We multiply parentheses

-129x^2+(2x+0.417)+3.5991

We get rid of parentheses

-129x^2+2x+0.417+3.5991

We add all the numbers together, and all the variables

-129x^2+2x+4.0161

Back to the equation:

-(-129x^2+2x+4.0161)


We get rid of parentheses

129x^2-2x-4.0161=0

a = 129; b = -2; c = -4.0161;
Δ = b2-4ac
Δ = -22-4·129·(-4.0161)
Δ = 2076.3076
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{-(-2)-\sqrt{2076.3076}}{2*129}=\frac{2-\sqrt{2076.3076}}{258}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{2076.3076}}{2*129}=\frac{2+\sqrt{2076.3076}}{258}
$