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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-30x)/3x^2+10x/3x^2-8=0

We multiply all the terms by the denominator


(-30x)+10x-8*3x^2=0

We add all the numbers together, and all the variables

10x+(-30x)-8*3x^2=0

Wy multiply elements

-24x^2+10x+(-30x)=0

We get rid of parentheses

-24x^2+10x-30x=0

We add all the numbers together, and all the variables

-24x^2-20x=0

a = -24; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-24)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-24}=\frac{40}{-48}
=-5/6
$