10/3x+1-6/5x=31/15

Solution for 10/3x+1-6/5x=31/15 equation:

10/3x+1-6/5x=31/15

We move all terms to the left:

10/3x+1-6/5x-(31/15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

10/3x-6/5x+1-(+31/15)=0

We get rid of parentheses

10/3x-6/5x+1-31/15=0

We calculate fractions


(-2325x^2)/225x^2+750x/225x^2+(-270x)/225x^2+1=0

We multiply all the terms by the denominator


(-2325x^2)+750x+(-270x)+1*225x^2=0

Wy multiply elements

(-2325x^2)+225x^2+750x+(-270x)=0

We get rid of parentheses

-2325x^2+225x^2+750x-270x=0

We add all the numbers together, and all the variables

-2100x^2+480x=0

a = -2100; b = 480; c = 0;
Δ = b2-4ac
Δ = 4802-4·(-2100)·0
Δ = 230400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{230400}=480$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-480}{2*-2100}=\frac{-960}{-4200}
=8/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+480}{2*-2100}=\frac{0}{-4200}
=0
$