2/3x+4-82=x

Solution for 2/3x+4-82=x equation:

2/3x+4-82=x

We move all terms to the left:

2/3x+4-82-(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

-1x+2/3x-78=0

We multiply all the terms by the denominator


-1x*3x-78*3x+2=0

Wy multiply elements

-3x^2-234x+2=0

a = -3; b = -234; c = +2;
Δ = b2-4ac
Δ = -2342-4·(-3)·2
Δ = 54780
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:

$\sqrt{\Delta}=\sqrt{54780}=\sqrt{4*13695}=\sqrt{4}*\sqrt{13695}=2\sqrt{13695}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-2\sqrt{13695}}{2*-3}=\frac{234-2\sqrt{13695}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+2\sqrt{13695}}{2*-3}=\frac{234+2\sqrt{13695}}{-6}
$