-3x-9=1/3x-39

Solution for -3x-9=1/3x-39 equation:

-3x-9=1/3x-39

We move all terms to the left:

-3x-9-(1/3x-39)=0


Domain of the equation: 3x-39)!=0

x∈R


We get rid of parentheses

-3x-1/3x+39-9=0

We multiply all the terms by the denominator


-3x*3x+39*3x-9*3x-1=0

Wy multiply elements

-9x^2+117x-27x-1=0

We add all the numbers together, and all the variables

-9x^2+90x-1=0

a = -9; b = 90; c = -1;
Δ = b2-4ac
Δ = 902-4·(-9)·(-1)
Δ = 8064
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:

$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-24\sqrt{14}}{2*-9}=\frac{-90-24\sqrt{14}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+24\sqrt{14}}{2*-9}=\frac{-90+24\sqrt{14}}{-18}
$