3/5x-8/3x=-31/15

Solution for 3/5x-8/3x=-31/15 equation:

3/5x-8/3x=-31/15

We move all terms to the left:

3/5x-8/3x-(-31/15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

3/5x-8/3x+31/15=0

We calculate fractions


1395x^2/225x^2+135x/225x^2+(-600x)/225x^2=0

We multiply all the terms by the denominator


1395x^2+135x+(-600x)=0

We get rid of parentheses

1395x^2+135x-600x=0

We add all the numbers together, and all the variables

1395x^2-465x=0

a = 1395; b = -465; c = 0;
Δ = b2-4ac
Δ = -4652-4·1395·0
Δ = 216225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{216225}=465$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-465)-465}{2*1395}=\frac{0}{2790}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-465)+465}{2*1395}=\frac{930}{2790}
=1/3
$