16-2x=2/3x+9

Solution for 16-2x=2/3x+9 equation:

16-2x=2/3x+9

We move all terms to the left:

16-2x-(2/3x+9)=0


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

x∈R


We get rid of parentheses

-2x-2/3x-9+16=0

We multiply all the terms by the denominator


-2x*3x-9*3x+16*3x-2=0

Wy multiply elements

-6x^2-27x+48x-2=0

We add all the numbers together, and all the variables

-6x^2+21x-2=0

a = -6; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·(-6)·(-2)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{393}}{2*-6}=\frac{-21-\sqrt{393}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{393}}{2*-6}=\frac{-21+\sqrt{393}}{-12}
$