61/9x+3/13x=281/3

Solution for 61/9x+3/13x=281/3 equation:

61/9x+3/13x=281/3

We move all terms to the left:

61/9x+3/13x-(281/3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R


We add all the numbers together, and all the variables

61/9x+3/13x-(+281/3)=0

We get rid of parentheses

61/9x+3/13x-281/3=0

We calculate fractions


(-32877x^2)/1053x^2+7137x/1053x^2+243x/1053x^2=0

We multiply all the terms by the denominator


(-32877x^2)+7137x+243x=0

We add all the numbers together, and all the variables

(-32877x^2)+7380x=0

We get rid of parentheses

-32877x^2+7380x=0

a = -32877; b = 7380; c = 0;
Δ = b2-4ac
Δ = 73802-4·(-32877)·0
Δ = 54464400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54464400}=7380$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7380)-7380}{2*-32877}=\frac{-14760}{-65754}
=820/3653
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7380)+7380}{2*-32877}=\frac{0}{-65754}
=0
$