-x+1=2/3x-9

Solution for -x+1=2/3x-9 equation:

-x+1=2/3x-9

We move all terms to the left:

-x+1-(2/3x-9)=0


Domain of the equation: 3x-9)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(2/3x-9)+1=0

We get rid of parentheses

-1x-2/3x+9+1=0

We multiply all the terms by the denominator


-1x*3x+9*3x+1*3x-2=0

Wy multiply elements

-3x^2+27x+3x-2=0

We add all the numbers together, and all the variables

-3x^2+30x-2=0

a = -3; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·(-3)·(-2)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{219}}{2*-3}=\frac{-30-2\sqrt{219}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{219}}{2*-3}=\frac{-30+2\sqrt{219}}{-6}
$