9+7/3x=x+11

Solution for 9+7/3x=x+11 equation:

9+7/3x=x+11

We move all terms to the left:

9+7/3x-(x+11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

7/3x-x-11+9=0

We multiply all the terms by the denominator


-x*3x-11*3x+9*3x+7=0

Wy multiply elements

-3x^2-33x+27x+7=0

We add all the numbers together, and all the variables

-3x^2-6x+7=0

a = -3; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-3)·7
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{30}}{2*-3}=\frac{6-2\sqrt{30}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{30}}{2*-3}=\frac{6+2\sqrt{30}}{-6}
$