1/3x+10=x-2

Solution for 1/3x+10=x-2 equation:

1/3x+10=x-2

We move all terms to the left:

1/3x+10-(x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+2+10=0

We multiply all the terms by the denominator


-x*3x+2*3x+10*3x+1=0

Wy multiply elements

-3x^2+6x+30x+1=0

We add all the numbers together, and all the variables

-3x^2+36x+1=0

a = -3; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-3)·1
Δ = 1308
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:

$\sqrt{\Delta}=\sqrt{1308}=\sqrt{4*327}=\sqrt{4}*\sqrt{327}=2\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{327}}{2*-3}=\frac{-36-2\sqrt{327}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{327}}{2*-3}=\frac{-36+2\sqrt{327}}{-6}
$