10-1/3x=8-1/5x

Solution for 10-1/3x=8-1/5x equation:

10-1/3x=8-1/5x

We move all terms to the left:

10-1/3x-(8-1/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x-(-1/5x+8)+10=0

We get rid of parentheses

-1/3x+1/5x-8+10=0

We calculate fractions


(-5x)/15x^2+3x/15x^2-8+10=0

We add all the numbers together, and all the variables

(-5x)/15x^2+3x/15x^2+2=0

We multiply all the terms by the denominator


(-5x)+3x+2*15x^2=0

We add all the numbers together, and all the variables

3x+(-5x)+2*15x^2=0

Wy multiply elements

30x^2+3x+(-5x)=0

We get rid of parentheses

30x^2+3x-5x=0

We add all the numbers together, and all the variables

30x^2-2x=0

a = 30; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·30·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*30}=\frac{4}{60}
=1/15
$