5/3x+2-x=15

Solution for 5/3x+2-x=15 equation:

5/3x+2-x=15

We move all terms to the left:

5/3x+2-x-(15)=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+5/3x-13=0

We multiply all the terms by the denominator


-1x*3x-13*3x+5=0

Wy multiply elements

-3x^2-39x+5=0

a = -3; b = -39; c = +5;
Δ = b2-4ac
Δ = -392-4·(-3)·5
Δ = 1581
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{-(-39)-\sqrt{1581}}{2*-3}=\frac{39-\sqrt{1581}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1581}}{2*-3}=\frac{39+\sqrt{1581}}{-6}
$