-7/3x+8/5=13/15x

Solution for -7/3x+8/5=13/15x equation:

-7/3x+8/5=13/15x

We move all terms to the left:

-7/3x+8/5-(13/15x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-7/3x-(+13/15x)+8/5=0

We get rid of parentheses

-7/3x-13/15x+8/5=0

We calculate fractions


360x^2/1125x^2+(-2625x)/1125x^2+(-975x)/1125x^2=0

We multiply all the terms by the denominator


360x^2+(-2625x)+(-975x)=0

We get rid of parentheses

360x^2-2625x-975x=0

We add all the numbers together, and all the variables

360x^2-3600x=0

a = 360; b = -3600; c = 0;
Δ = b2-4ac
Δ = -36002-4·360·0
Δ = 12960000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12960000}=3600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3600)-3600}{2*360}=\frac{0}{720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3600)+3600}{2*360}=\frac{7200}{720}
=10
$