17-x=1/3x+15+6

Solution for 17-x=1/3x+15+6 equation:

17-x=1/3x+15+6

We move all terms to the left:

17-x-(1/3x+15+6)=0


Domain of the equation: 3x+15+6)!=0

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

3x+6)!=-15

x∈R


We add all the numbers together, and all the variables

-x-(1/3x+21)+17=0

We add all the numbers together, and all the variables

-1x-(1/3x+21)+17=0

We get rid of parentheses

-1x-1/3x-21+17=0

We multiply all the terms by the denominator


-1x*3x-21*3x+17*3x-1=0

Wy multiply elements

-3x^2-63x+51x-1=0

We add all the numbers together, and all the variables

-3x^2-12x-1=0

a = -3; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-3)·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*-3}=\frac{12-2\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*-3}=\frac{12+2\sqrt{33}}{-6}
$