8/x+6=3/2x-12-1

Solution for 8/x+6=3/2x-12-1 equation:

8/x+6=3/2x-12-1

We move all terms to the left:

8/x+6-(3/2x-12-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-12-1)!=0

We move all terms containing x to the left, all other terms to the right

2x-1)!=12

x∈R


We add all the numbers together, and all the variables

8/x-(3/2x-13)+6=0

We get rid of parentheses

8/x-3/2x+13+6=0

We calculate fractions


16x/2x^2+(-3x)/2x^2+13+6=0

We add all the numbers together, and all the variables

16x/2x^2+(-3x)/2x^2+19=0

We multiply all the terms by the denominator


16x+(-3x)+19*2x^2=0

Wy multiply elements

38x^2+16x+(-3x)=0

We get rid of parentheses

38x^2+16x-3x=0

We add all the numbers together, and all the variables

38x^2+13x=0

a = 38; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·38·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*38}=\frac{-26}{76}
=-13/38
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*38}=\frac{0}{76}
=0
$