-1/3x+6.7=3x

Solution for -1/3x+6.7=3x equation:

-1/3x+6.7=3x

We move all terms to the left:

-1/3x+6.7-(3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3x-1/3x+6.7=0

We multiply all the terms by the denominator


-3x*3x+(6.7)*3x-1=0

We multiply parentheses

-3x*3x+20.1x-1=0

Wy multiply elements

-9x^2+20.1x-1=0

a = -9; b = 20.1; c = -1;
Δ = b2-4ac
Δ = 20.12-4·(-9)·(-1)
Δ = 368.01
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{-(20.1)-\sqrt{368.01}}{2*-9}=\frac{-20.1-\sqrt{368.01}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20.1)+\sqrt{368.01}}{2*-9}=\frac{-20.1+\sqrt{368.01}}{-18}
$