(x+5)/(x+3)=4,76/x

Solution for (x+5)/(x+3)=4,76/x equation:

(x+5)/(x+3)=4.76/x

We move all terms to the left:

(x+5)/(x+3)-(4.76/x)=0


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

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

x!=-3

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(x+5)/(x+3)-(+4.76/x)=0

We get rid of parentheses

(x+5)/(x+3)-4.76/x=0

We calculate fractions


(x^2+5x)/(x^2+3x)+(-4.76x-14.28)/(x^2+3x)=0

We multiply all the terms by the denominator


(x^2+5x)+(-4.76x-14.28)=0

We get rid of parentheses

x^2+5x-4.76x-14.28=0

We add all the numbers together, and all the variables

x^2+0.24x-14.28=0

a = 1; b = 0.24; c = -14.28;
Δ = b2-4ac
Δ = 0.242-4·1·(-14.28)
Δ = 57.1776
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{-(0.24)-\sqrt{57.1776}}{2*1}=\frac{-0.24-\sqrt{57.1776}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.24)+\sqrt{57.1776}}{2*1}=\frac{-0.24+\sqrt{57.1776}}{2}
$