1/3x=-x-10

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

1/3x=-x-10

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3x+1x+10=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+30x+1=0

a = 3; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·3·1
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{222}}{2*3}=\frac{-30-2\sqrt{222}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{222}}{2*3}=\frac{-30+2\sqrt{222}}{6}
$