10-x/12x=8/3x

Solution for 10-x/12x=8/3x equation:

10-x/12x=8/3x

We move all terms to the left:

10-x/12x-(8/3x)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x/12x-(+8/3x)+10=0

We get rid of parentheses

-x/12x-8/3x+10=0

We calculate fractions


(-3x^2)/36x^2+(-96x)/36x^2+10=0

We multiply all the terms by the denominator


(-3x^2)+(-96x)+10*36x^2=0

Wy multiply elements

(-3x^2)+360x^2+(-96x)=0

We get rid of parentheses

-3x^2+360x^2-96x=0

We add all the numbers together, and all the variables

357x^2-96x=0

a = 357; b = -96; c = 0;
Δ = b2-4ac
Δ = -962-4·357·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-96}{2*357}=\frac{0}{714}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+96}{2*357}=\frac{192}{714}
=32/119
$