-1/3x+2=5+5x

Solution for -1/3x+2=5+5x equation:

-1/3x+2=5+5x

We move all terms to the left:

-1/3x+2-(5+5x)=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-(5x+5)+2=0

We get rid of parentheses

-1/3x-5x-5+2=0

We multiply all the terms by the denominator


-5x*3x-5*3x+2*3x-1=0

Wy multiply elements

-15x^2-15x+6x-1=0

We add all the numbers together, and all the variables

-15x^2-9x-1=0

a = -15; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·(-15)·(-1)
Δ = 21
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{-(-9)-\sqrt{21}}{2*-15}=\frac{9-\sqrt{21}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{21}}{2*-15}=\frac{9+\sqrt{21}}{-30}
$