6x+27/9x+x-6/3+3=15

Solution for 6x+27/9x+x-6/3+3=15 equation:

6x+27/9x+x-6/3+3=15

We move all terms to the left:

6x+27/9x+x-6/3+3-(15)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


determiningTheFunctionDomain
6x+27/9x+x+3-15-6/3=0

We add all the numbers together, and all the variables

7x+27/9x-14=0

We multiply all the terms by the denominator


7x*9x-14*9x+27=0

Wy multiply elements

63x^2-126x+27=0

a = 63; b = -126; c = +27;
Δ = b2-4ac
Δ = -1262-4·63·27
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-36\sqrt{7}}{2*63}=\frac{126-36\sqrt{7}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+36\sqrt{7}}{2*63}=\frac{126+36\sqrt{7}}{126}
$