/(x+6)+(x+3)+9x=30-7x

Solution for /(x+6)+(x+3)+9x=30-7x equation:

/(x+6)+(x+3)+9x=30-7x

We move all terms to the left:

/(x+6)+(x+3)+9x-(30-7x)=0


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

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

x!=-6

x∈R


We add all the numbers together, and all the variables

/(x+6)+(x+3)+9x-(-7x+30)=0

We add all the numbers together, and all the variables

9x+/(x+6)+(x+3)-(-7x+30)=0

We get rid of parentheses

9x+/(x+6)+x+7x+3-30=0

We multiply all the terms by the denominator


9x*(x+6)+x*(x+6)+7x*(x+6)+3*(x+6)-30*(x+6)+=0

We add all the numbers together, and all the variables

9x*(x+6)+x*(x+6)+7x*(x+6)+3*(x+6)-30*(x+6)=0

We multiply parentheses

9x^2+x^2+7x^2+54x+6x+42x+3x-30x+18-180=0

We add all the numbers together, and all the variables

17x^2+75x-162=0

a = 17; b = 75; c = -162;
Δ = b2-4ac
Δ = 752-4·17·(-162)
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-129}{2*17}=\frac{-204}{34}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+129}{2*17}=\frac{54}{34}
=1+10/17
$