7x=8/x-6

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

7x=8/x-6

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

7x-8/x+6=0

We multiply all the terms by the denominator


7x*x+6*x-8=0

We add all the numbers together, and all the variables

6x+7x*x-8=0

Wy multiply elements

7x^2+6x-8=0

a = 7; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·7·(-8)
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{65}}{2*7}=\frac{-6-2\sqrt{65}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{65}}{2*7}=\frac{-6+2\sqrt{65}}{14}
$