10/x-6=1/2x+7

Solution for 10/x-6=1/2x+7 equation:

10/x-6=1/2x+7

We move all terms to the left:

10/x-6-(1/2x+7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

10/x-1/2x-7-6=0

We calculate fractions


20x/2x^2+(-x)/2x^2-7-6=0

We add all the numbers together, and all the variables

20x/2x^2+(-1x)/2x^2-7-6=0

We add all the numbers together, and all the variables

20x/2x^2+(-1x)/2x^2-13=0

We multiply all the terms by the denominator


20x+(-1x)-13*2x^2=0

Wy multiply elements

-26x^2+20x+(-1x)=0

We get rid of parentheses

-26x^2+20x-1x=0

We add all the numbers together, and all the variables

-26x^2+19x=0

a = -26; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-26)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-26}=\frac{-38}{-52}
=19/26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-26}=\frac{0}{-52}
=0
$