296/x+200/(x+3)=13

Solution for 296/x+200/(x+3)=13 equation:

296/x+200/(x+3)=13

We move all terms to the left:

296/x+200/(x+3)-(13)=0


Domain of the equation: x!=0

x∈R



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


We calculate fractions


(296x+888)/(x^2+3x)+200x/(x^2+3x)-13=0

We multiply all the terms by the denominator


(296x+888)+200x-13*(x^2+3x)=0

We add all the numbers together, and all the variables

200x+(296x+888)-13*(x^2+3x)=0

We multiply parentheses

-13x^2+200x+(296x+888)-39x=0

We get rid of parentheses

-13x^2+200x+296x-39x+888=0

We add all the numbers together, and all the variables

-13x^2+457x+888=0

a = -13; b = 457; c = +888;
Δ = b2-4ac
Δ = 4572-4·(-13)·888
Δ = 255025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{255025}=505$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(457)-505}{2*-13}=\frac{-962}{-26}
=+37
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(457)+505}{2*-13}=\frac{48}{-26}
=-1+11/13
$