61/15x-32/3x=311/5

Solution for 61/15x-32/3x=311/5 equation:

61/15x-32/3x=311/5

We move all terms to the left:

61/15x-32/3x-(311/5)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

61/15x-32/3x-(+311/5)=0

We get rid of parentheses

61/15x-32/3x-311/5=0

We calculate fractions


(-41985x^2)/1125x^2+4575x/1125x^2+(-12000x)/1125x^2=0

We multiply all the terms by the denominator


(-41985x^2)+4575x+(-12000x)=0

We get rid of parentheses

-41985x^2+4575x-12000x=0

We add all the numbers together, and all the variables

-41985x^2-7425x=0

a = -41985; b = -7425; c = 0;
Δ = b2-4ac
Δ = -74252-4·(-41985)·0
Δ = 55130625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{55130625}=7425$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7425)-7425}{2*-41985}=\frac{0}{-83970}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7425)+7425}{2*-41985}=\frac{14850}{-83970}
=-55/311
$