7+2/3x-35=x

Solution for 7+2/3x-35=x equation:

7+2/3x-35=x

We move all terms to the left:

7+2/3x-35-(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-28=0

We multiply all the terms by the denominator


-1x*3x-28*3x+2=0

Wy multiply elements

-3x^2-84x+2=0

a = -3; b = -84; c = +2;
Δ = b2-4ac
Δ = -842-4·(-3)·2
Δ = 7080
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:

$\sqrt{\Delta}=\sqrt{7080}=\sqrt{4*1770}=\sqrt{4}*\sqrt{1770}=2\sqrt{1770}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1770}}{2*-3}=\frac{84-2\sqrt{1770}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1770}}{2*-3}=\frac{84+2\sqrt{1770}}{-6}
$