x/9x-30+6x=4+14-x

Solution for x/9x-30+6x=4+14-x equation:

x/9x-30+6x=4+14-x

We move all terms to the left:

x/9x-30+6x-(4+14-x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

x/9x+6x-(-1x+18)-30=0

We add all the numbers together, and all the variables

6x+x/9x-(-1x+18)-30=0

We get rid of parentheses

6x+x/9x+1x-18-30=0

We multiply all the terms by the denominator


6x*9x+x+1x*9x-18*9x-30*9x=0

We add all the numbers together, and all the variables

x+6x*9x+1x*9x-18*9x-30*9x=0

Wy multiply elements

54x^2+9x^2+x-162x-270x=0

We add all the numbers together, and all the variables

63x^2-431x=0

a = 63; b = -431; c = 0;
Δ = b2-4ac
Δ = -4312-4·63·0
Δ = 185761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{185761}=431$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-431)-431}{2*63}=\frac{0}{126}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-431)+431}{2*63}=\frac{862}{126}
=6+53/63
$