(1/6)3x-7=67x-3

Solution for (1/6)3x-7=67x-3 equation:

(1/6)3x-7=67x-3

We move all terms to the left:

(1/6)3x-7-(67x-3)=0


Domain of the equation: 6)3x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/6)3x-(67x-3)-7=0

We multiply parentheses

3x^2-(67x-3)-7=0

We get rid of parentheses

3x^2-67x+3-7=0

We add all the numbers together, and all the variables

3x^2-67x-4=0

a = 3; b = -67; c = -4;
Δ = b2-4ac
Δ = -672-4·3·(-4)
Δ = 4537
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{-(-67)-\sqrt{4537}}{2*3}=\frac{67-\sqrt{4537}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+\sqrt{4537}}{2*3}=\frac{67+\sqrt{4537}}{6}
$