33/5x-81/3=x

Solution for 33/5x-81/3=x equation:

33/5x-81/3=x

We move all terms to the left:

33/5x-81/3-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+33/5x-27=0

We multiply all the terms by the denominator


-1x*5x-27*5x+33=0

Wy multiply elements

-5x^2-135x+33=0

a = -5; b = -135; c = +33;
Δ = b2-4ac
Δ = -1352-4·(-5)·33
Δ = 18885
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{-(-135)-\sqrt{18885}}{2*-5}=\frac{135-\sqrt{18885}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18885}}{2*-5}=\frac{135+\sqrt{18885}}{-10}
$