5/2x-13/6x=32/15

Solution for 5/2x-13/6x=32/15 equation:

5/2x-13/6x=32/15

We move all terms to the left:

5/2x-13/6x-(32/15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-13/6x-(+32/15)=0

We get rid of parentheses

5/2x-13/6x-32/15=0

We calculate fractions


(-2304x^2)/180x^2+450x/180x^2+(-390x)/180x^2=0

We multiply all the terms by the denominator


(-2304x^2)+450x+(-390x)=0

We get rid of parentheses

-2304x^2+450x-390x=0

We add all the numbers together, and all the variables

-2304x^2+60x=0

a = -2304; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-2304)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-2304}=\frac{-120}{-4608}
=5/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-2304}=\frac{0}{-4608}
=0
$