-1/3x-6=3x-30

Solution for -1/3x-6=3x-30 equation:

-1/3x-6=3x-30

We move all terms to the left:

-1/3x-6-(3x-30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x-3x+30-6=0

We multiply all the terms by the denominator


-3x*3x+30*3x-6*3x-1=0

Wy multiply elements

-9x^2+90x-18x-1=0

We add all the numbers together, and all the variables

-9x^2+72x-1=0

a = -9; b = 72; c = -1;
Δ = b2-4ac
Δ = 722-4·(-9)·(-1)
Δ = 5148
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:

$\sqrt{\Delta}=\sqrt{5148}=\sqrt{36*143}=\sqrt{36}*\sqrt{143}=6\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{143}}{2*-9}=\frac{-72-6\sqrt{143}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{143}}{2*-9}=\frac{-72+6\sqrt{143}}{-18}
$