9+2/3x=1+x

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

9+2/3x=1+x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-3x^2+24x+2=0

a = -3; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·(-3)·2
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*-3}=\frac{-24-10\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*-3}=\frac{-24+10\sqrt{6}}{-6}
$