8-2/3x=2x-16

Solution for 8-2/3x=2x-16 equation:

8-2/3x=2x-16

We move all terms to the left:

8-2/3x-(2x-16)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-2/3x-2x+16+8=0

We multiply all the terms by the denominator


-2x*3x+16*3x+8*3x-2=0

Wy multiply elements

-6x^2+48x+24x-2=0

We add all the numbers together, and all the variables

-6x^2+72x-2=0

a = -6; b = 72; c = -2;
Δ = b2-4ac
Δ = 722-4·(-6)·(-2)
Δ = 5136
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:

$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{321}}{2*-6}=\frac{-72-4\sqrt{321}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{321}}{2*-6}=\frac{-72+4\sqrt{321}}{-12}
$