3/2x+7=8/x+6

Solution for 3/2x+7=8/x+6 equation:

3/2x+7=8/x+6

We move all terms to the left:

3/2x+7-(8/x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+6)!=0

x∈R


We get rid of parentheses

3/2x-8/x-6+7=0

We calculate fractions


3x/2x^2+(-16x)/2x^2-6+7=0

We add all the numbers together, and all the variables

3x/2x^2+(-16x)/2x^2+1=0

We multiply all the terms by the denominator


3x+(-16x)+1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-13x=0

a = 2; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·2·0
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*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*2}=\frac{26}{4}
=6+1/2
$