10.5-x+31/3x=2

Solution for 10.5-x+31/3x=2 equation:

10.5-x+31/3x=2

We move all terms to the left:

10.5-x+31/3x-(2)=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+31/3x+8.5=0

We multiply all the terms by the denominator


-1x*3x+(8.5)*3x+31=0

We multiply parentheses

-1x*3x+25.5x+31=0

Wy multiply elements

-3x^2+25.5x+31=0

a = -3; b = 25.5; c = +31;
Δ = b2-4ac
Δ = 25.52-4·(-3)·31
Δ = 1022.25
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{-(25.5)-\sqrt{1022.25}}{2*-3}=\frac{-25.5-\sqrt{1022.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25.5)+\sqrt{1022.25}}{2*-3}=\frac{-25.5+\sqrt{1022.25}}{-6}
$