10/x-28=2/3x

Solution for 10/x-28=2/3x equation:

10/x-28=2/3x

We move all terms to the left:

10/x-28-(2/3x)=0


Domain of the equation: 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

10/x-(+2/3x)-28=0

We get rid of parentheses

10/x-2/3x-28=0

We calculate fractions


30x/3x^2+(-2x)/3x^2-28=0

We multiply all the terms by the denominator


30x+(-2x)-28*3x^2=0

Wy multiply elements

-84x^2+30x+(-2x)=0

We get rid of parentheses

-84x^2+30x-2x=0

We add all the numbers together, and all the variables

-84x^2+28x=0

a = -84; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-84)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-84}=\frac{-56}{-168}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-84}=\frac{0}{-168}
=0
$