61/9x+31/2x=281/3

Solution for 61/9x+31/2x=281/3 equation:

61/9x+31/2x=281/3

We move all terms to the left:

61/9x+31/2x-(281/3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

61/9x+31/2x-(+281/3)=0

We get rid of parentheses

61/9x+31/2x-281/3=0

We calculate fractions


(-10116x^2)/162x^2+1098x/162x^2+2511x/162x^2=0

We multiply all the terms by the denominator


(-10116x^2)+1098x+2511x=0

We add all the numbers together, and all the variables

(-10116x^2)+3609x=0

We get rid of parentheses

-10116x^2+3609x=0

a = -10116; b = 3609; c = 0;
Δ = b2-4ac
Δ = 36092-4·(-10116)·0
Δ = 13024881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13024881}=3609$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3609)-3609}{2*-10116}=\frac{-7218}{-20232}
=401/1124
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3609)+3609}{2*-10116}=\frac{0}{-20232}
=0
$