1/3x+20=3x-85

Solution for 1/3x+20=3x-85 equation:

1/3x+20=3x-85

We move all terms to the left:

1/3x+20-(3x-85)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-3x+85+20=0

We multiply all the terms by the denominator


-3x*3x+85*3x+20*3x+1=0

Wy multiply elements

-9x^2+255x+60x+1=0

We add all the numbers together, and all the variables

-9x^2+315x+1=0

a = -9; b = 315; c = +1;
Δ = b2-4ac
Δ = 3152-4·(-9)·1
Δ = 99261
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:

$\sqrt{\Delta}=\sqrt{99261}=\sqrt{9*11029}=\sqrt{9}*\sqrt{11029}=3\sqrt{11029}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-3\sqrt{11029}}{2*-9}=\frac{-315-3\sqrt{11029}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+3\sqrt{11029}}{2*-9}=\frac{-315+3\sqrt{11029}}{-18}
$