63x/(13-17x)-6x=63

Solution for 63x/(13-17x)-6x=63 equation:

63x/(13-17x)-6x=63

We move all terms to the left:

63x/(13-17x)-6x-(63)=0


Domain of the equation: (13-17x)!=0

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

-17x!=-13

x!=-13/-17

x!=13/17

x∈R


We add all the numbers together, and all the variables

63x/(-17x+13)-6x-63=0

We add all the numbers together, and all the variables

-6x+63x/(-17x+13)-63=0

We multiply all the terms by the denominator


-6x*(-17x+13)+63x-63*(-17x+13)=0

We add all the numbers together, and all the variables

63x-6x*(-17x+13)-63*(-17x+13)=0

We multiply parentheses

102x^2+63x-78x+1071x-819=0

We add all the numbers together, and all the variables

102x^2+1056x-819=0

a = 102; b = 1056; c = -819;
Δ = b2-4ac
Δ = 10562-4·102·(-819)
Δ = 1449288
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:

$\sqrt{\Delta}=\sqrt{1449288}=\sqrt{36*40258}=\sqrt{36}*\sqrt{40258}=6\sqrt{40258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1056)-6\sqrt{40258}}{2*102}=\frac{-1056-6\sqrt{40258}}{204}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1056)+6\sqrt{40258}}{2*102}=\frac{-1056+6\sqrt{40258}}{204}
$