7/x=8/5x-6

Solution for 7/x=8/5x-6 equation:

7/x=8/5x-6

We move all terms to the left:

7/x-(8/5x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-6)!=0

x∈R


We get rid of parentheses

7/x-8/5x+6=0

We calculate fractions


35x/5x^2+(-8x)/5x^2+6=0

We multiply all the terms by the denominator


35x+(-8x)+6*5x^2=0

Wy multiply elements

30x^2+35x+(-8x)=0

We get rid of parentheses

30x^2+35x-8x=0

We add all the numbers together, and all the variables

30x^2+27x=0

a = 30; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·30·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*30}=\frac{-54}{60}
=-9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*30}=\frac{0}{60}
=0
$