15+7x=-6/x-6+x-6=x-6

Solution for 15+7x=-6/x-6+x-6=x-6 equation:

15+7x=-6/x-6+x-6=x-6

We move all terms to the left:

15+7x-(-6/x-6+x-6)=0


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

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

x+x-6)!=6

x∈R


We add all the numbers together, and all the variables

7x-(x-6/x-12)+15=0

We get rid of parentheses

7x-x+6/x+12+15=0

We multiply all the terms by the denominator


7x*x-x*x+12*x+15*x+6=0

We add all the numbers together, and all the variables

27x+7x*x-x*x+6=0

Wy multiply elements

7x^2-1x^2+27x+6=0

We add all the numbers together, and all the variables

6x^2+27x+6=0

a = 6; b = 27; c = +6;
Δ = b2-4ac
Δ = 272-4·6·6
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{65}}{2*6}=\frac{-27-3\sqrt{65}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{65}}{2*6}=\frac{-27+3\sqrt{65}}{12}
$