-7/x=-10/3x+7

Solution for -7/x=-10/3x+7 equation:

-7/x=-10/3x+7

We move all terms to the left:

-7/x-(-10/3x+7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+7)!=0

x∈R


We get rid of parentheses

-7/x+10/3x-7=0

We calculate fractions


(-21x)/3x^2+10x/3x^2-7=0

We multiply all the terms by the denominator


(-21x)+10x-7*3x^2=0

We add all the numbers together, and all the variables

10x+(-21x)-7*3x^2=0

Wy multiply elements

-21x^2+10x+(-21x)=0

We get rid of parentheses

-21x^2+10x-21x=0

We add all the numbers together, and all the variables

-21x^2-11x=0

a = -21; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-21)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-21}=\frac{22}{-42}
=-11/21
$